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Sherratt, Jonathan A.

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 Author ID: sherratt.jonathan-a Published as: Sherratt, Jonathan A.; Sherratt, J. A.; Sherratt, Jonathan External Links: MGP
 Documents Indexed: 124 Publications since 1991
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Co-Authors

 38 single-authored 20 Maini, Philip Kumar 9 Painter, Kevin J. 8 Olsen, Luke 7 Smith, Matthew J. 5 Armstrong, Nicola J. 5 Dale, Paul D. 5 Owen, Markus Roger 4 Bennett, Jamie J. R. 4 Benson, Debbie L. 4 Dallon, John C. 4 Eigentler, Lukas 4 Marchant, Ben P. 3 Chaplain, Mark A. J. 3 Kay, Alison L. 3 Murray, James Dickson 3 Norbury, John W. 3 Rademacher, Jens Diederich Michael 3 Webb, Steven D. 2 Bianchi, Arianna 2 Bloomfield, J. M. 2 Dagbovie, Ayawoa S. 2 Hofer, Thomas 2 Lewis, Julian 2 Perumpanani, Abbey J. 2 Reynolds, Jennifer J. H. 2 Taylor, Rachel A. 2 Wearing, Helen J. 1 Anderson, Alexander R. A. 1 Arnold, Frank 1 Boots, Mike 1 Brezhnev, Yurii V. 1 Byrne, Helen Mary 1 Cobbold, Christina A. 1 Fish, Reginald G. 1 Fowler, Andrew C. 1 Gaffney, Eamonn A. 1 Gerisch, Alf 1 Gourley, Stephen A. 1 Hilker, Frank M. 1 Lambin, Xavier 1 Lewis, Mark Alun 1 Liu, Quanxing 1 Lord, Gabriel James 1 Mackenzie, Julia J. 1 Maxwell, S. R. J. 1 McDougall, Steven R. 1 McLeod, John Bryce 1 Métevier, D. 1 Monk, Nicholas A. M. 1 Montes, P. C. 1 Perumpanai, Abbey J. 1 Savill, Nicholas J. 1 Sneyd, James 1 Synodinos, Alexios D. 1 van de Koppel, Johan 1 Waugh, Helen V. 1 Wearning, Helen J. 1 Weller, Richard
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Serials

 18 Bulletin of Mathematical Biology 13 SIAM Journal on Applied Mathematics 12 Journal of Mathematical Biology 11 Journal of Theoretical Biology 10 Physica D 6 IMA Journal of Applied Mathematics 6 Mathematical Biosciences 5 IMA Journal of Mathematics Applied in Medicine and Biology 5 Applied Mathematics Letters 4 Nonlinearity 4 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Mathematical and Computer Modelling 3 SIAM Journal on Applied Dynamical Systems 2 Dynamics and Stability of Systems 2 European Journal of Applied Mathematics 2 Proceedings of the National Academy of Sciences of the United States of America 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Journal of Theoretical Medicine 2 Forma 2 Mathematical Modelling of Natural Phenomena 1 Applied Mathematics and Computation 1 Theoretical Population Biology 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Nonlinear Science 1 Advances in Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Nonlinear Analysis. Theory, Methods & Applications
all top 5

Fields

 100 Biology and other natural sciences (92-XX) 84 Partial differential equations (35-XX) 14 Ordinary differential equations (34-XX) 13 Numerical analysis (65-XX) 9 Dynamical systems and ergodic theory (37-XX) 4 Integral equations (45-XX) 3 Fluid mechanics (76-XX) 2 Difference and functional equations (39-XX) 1 Special functions (33-XX) 1 Computer science (68-XX) 1 Statistical mechanics, structure of matter (82-XX)

Citations contained in zbMATH Open

118 Publications have been cited 1,476 times in 867 Documents Cited by Year
A new mathematical model for avascular tumour growth. Zbl 0990.92021
Sherratt, Jonathan A.; Chaplain, Mark A. J.
2001
Ecological chaos in the wake of invasion. Zbl 0819.92024
Sherratt, Jonathan; Lewis, Mark A.; Fowler, Andrew C.
1995
An analysis of vegetation stripe formation in semi-arid landscapes. Zbl 1068.92047
Sherratt, Jonathan A.
2005
Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Zbl 1334.92106
McDougall, S. R.; Anderson, A. R. A.; Chaplain, M. A. J.; Sherratt, J. A.
2002
A nonlocal model for contact attraction and repulsion in heterogeneous cell populations. Zbl 1335.92026
Painter, K. J.; Bloomfield, J. M.; Sherratt, J. A.; Gerisch, A.
2015
Diffusion driven instability in an inhomogeneous domain. Zbl 0758.92003
Benson, Debbie L.; Sherratt, Jonathan A.; Maini, Philip K.
1993
Mathematical analysis of a basic model for epidermal wound healing. Zbl 0721.92010
Sherratt, J. A.; Murray, J. D.
1991
Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments. Zbl 1118.92064
Sherratt, Jonathan A.; Lord, Gabriel J.
2007
A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion. Zbl 1001.92523
Perumpanai, Abbey J.; Sherratt, Jonathan; Norbury, John; Byrne, Helen M.
1999
Travelling wave solutions to a haptotaxis-dominated model of malignant invasion. Zbl 0985.92012
Marchant, B. P.; Norbury, J.; Sherratt, J. A.
2001
Cellular pattern formation during Dictyostelium aggregation. Zbl 0888.92005
Höfer, Thomas; Sherratt, Jonathan A.; Maini, Philip K.
1995
On the transition from initial data to travelling waves in the Fisher-KPP equation. Zbl 0912.35084
Sherratt, Jonathan A.
1998
Wavefront propagation in a competition equation with a new motility term modelling contact inhibition between cell populations. Zbl 1005.76098
Sherratt, Jonathan A.
2000
Mathematical modeling of corneal epithelial wound healing. Zbl 0818.92007
Dale, Paul D.; Maini, Philip K.; Sherratt, Jonathan A.
1994
Modelling the macrophage invasion of tumours: Effects on growth and composition. Zbl 0909.92022
Owen, Markus R.; Sherratt, Jonathan A.
1998
Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. I. Zbl 1197.92047
Sherratt, Jonathan A.
2010
Boundedness of solutions of a non-local reaction-diffusion model for adhesion in cell aggregation and cancer invasion. Zbl 1194.35219
Sherratt, Jonathan A.; Gourley, Stephen A.; Armstrong, Nicola J.; Painter, Kevin J.
2009
Algebraic decay and variable speeds in wavefront solutions of a scalar reaction-diffusion equation. Zbl 0858.35062
Sherratt, Jonathan A.; Marchant, Ben P.
1996
Mathematical modelling of macrophage dynamics in tumours. Zbl 0932.92019
Owen, Markus R.; Sherratt, Jonathan A.
1999
Unravelling the Turing bifurcation using spatially varying diffusion coefficients. Zbl 0919.92006
Benson, Debbie L.; Maini, Philip K.; Sherratt, Jonathan A.
1998
Chemotaxis and chemokinesis in eukaryotic cells: The Keller-Segel equations as an approximation to a detailed model. Zbl 0789.92017
Sherratt, Jonathan A.
1994
On the evolution of periodic plane waves in reaction-diffusion systems of $$\lambda -\omega$$ type. Zbl 0806.35080
Sherratt, Jonathan A.
1994
Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments. V: The transition from patterns to desert. Zbl 1320.92078
Sherratt, Jonathan A.
2013
Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach. Zbl 1334.92131
Cobbold, C. A.; Sherratt, J. A.; Maxwell, S. R. J.
2002
The impact of adhesion on cellular invasion processes in cancer and development. Zbl 1406.92156
Painter, Kevin J.; Armstrong, Nicola J.; Sherratt, Jonathan A.
2010
A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis. Zbl 0891.92016
Olsen, Luke; Sherratt, Jonathan A.; Maini, Philip K.; Arnold, Frank
1997
Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. II: Patterns with the largest possible propagation speeds. Zbl 1239.92085
Sherratt, Jonathan A.
2011
Adding adhesion to a chemical signaling model for somite formation. Zbl 1169.92008
Armstrong, Nicola J.; Painter, Kevin J.; Sherratt, Jonathan A.
2009
Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations. Zbl 1244.65155
Sherratt, Jonathan A.
2012
Nonsharp travelling wave fronts in the Fisher equation with degenerate nonlinear diffusion. Zbl 0903.35026
Sherratt, J. A.; Marchant, B. P.
1996
A continuum approach to modelling cell-cell adhesion. Zbl 1447.92113
Armstrong, Nicola J.; Painter, Kevin J.; Sherratt, Jonathan A.
2006
Pattern formation in reaction-diffusion models with spatially inhomogeneous diffusion coefficients. Zbl 0767.92004
Maini, Philip K.; Benson, Debbie L.; Sherratt, Jonathan A.
1992
The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems. Zbl 1361.34040
Smith, Matthew J.; Sherratt, Jonathan A.
2007
Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion. Zbl 1203.37062
Sherratt, Jonathan A.; Smith, Matthew J.; Rademacher, Jens D. M.
2009
Invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave. Zbl 0940.35111
Sherratt, Jonathan A.
1998
A mathematical model for fibro-proliferative wound healing disorders. Zbl 0865.92010
Olsen, Luke; Sherratt, Jonathan A.; Maini, Philip K.
1996
Absolute stability of wavetrains can explain spatiotemporal dynamics in reaction-diffusion systems of lambda-omega type. Zbl 1183.35032
Smith, Matthew J.; Rademacher, Jens D. M.; Sherratt, Jonathan A.
2009
Invasion generates periodic traveling waves (wavetrains) in predator-prey models with nonlocal dispersal. Zbl 1382.35323
Sherratt, Jonathan A.
2016
Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments. IV: Slowly moving patterns and their stability. Zbl 1321.92083
Sherratt, Jonathan A.
2013
On the propagation of calcium waves in an inhomogeneous medium. Zbl 0866.35128
Sneyd, James; Sherratt, Jonathan
1997
Phase differences in reaction-diffusion-advection systems and applications to morphogenesis. Zbl 0843.35041
Perumpanani, Abbey J.; Sherratt, Jonathan A.; Maini, Philip K.
1995
A mathematical biologist’s guide to absolute and convective instability. Zbl 1283.92007
Sherratt, Jonathan A.; Dagbovie, Ayawoa S.; Hilker, Frank M.
2014
Turing bifurcations with a temporally varying diffusion coefficient. Zbl 0812.92024
Sherratt, Jonathan A.
1995
Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. III: The transition between homoclinic solutions. Zbl 1261.35144
Sherratt, Jonathan A.
2013
Traveling wave solutions of a mathematical model for tumor encapsulation. Zbl 1012.92018
Sherratt, Jonathan A.
2000
Absolute stability and dynamical stabilisation in predator-prey systems. Zbl 1284.92109
Dagbovie, Ayawoa S.; Sherratt, Jonathan A.
2014
Analysis of a model for banded vegetation patterns in semi-arid environments with nonlocal dispersal. Zbl 1453.35025
Eigentler, Lukas; Sherratt, Jonathan A.
2018
Spatially varying equilibria of mechanical models: Application to dermal wound contraction. Zbl 0888.92021
Olsen, Luke; Maini, Philip K.; Sherratt, Jonathan A.
1998
Mathematical modelling of juxtacrine cell signalling. Zbl 0940.92009
Owen, Markus R.; Sherratt, Jonathan A.
1998
Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients. Zbl 0784.92004
Benson, D. L.; Maini, P. K.; Sherratt, J. A.
1993
Modelling the movement of interacting cell populations. Zbl 1464.92050
Painter, Kevin J.; Sherratt, Jonathan A.
2003
Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations. Zbl 1271.65132
Sherratt, Jonathan A.
2013
Comparison theorems and variable speed waves for a scalar reaction-diffusion equation. Zbl 0996.35034
Kay, Alison L.; Sherratt, Jonathan A.; McLeod, J. B.
2001
A mathematical model for fibroblast and collagen orientation. Zbl 0909.92014
Dallon, John C.; Sherratt, Jonathan A.
1998
On the form of smooth-front travelling waves in a reaction-diffusion equation with degenerate nonlinear diffusion. Zbl 1202.35050
Sherratt, J. A.
2010
Mathematical modelling of anisotropy in fibrous connective tissue. Zbl 0953.92011
Olsen, Luke; Maini, Philip K.; Sherratt, Jonathan A.; Dallon, John
1999
Unstable wavetrains and chaotic wakes in reaction-diffusion systems of $$\lambda-\omega$$ type. Zbl 0900.35194
Sherratt, Jonathan A.
1995
A mathematical model for lymphangiogenesis in normal and diabetic wounds. Zbl 1343.92062
Bianchi, Arianna; Painter, Kevin J.; Sherratt, Jonathan A.
2015
Mathematical modelling of capsule formation and multinodularity in benign tumour growth. Zbl 0910.92017
Perumpanani, Abbey J.; Sherratt, Jonathan A.; Norbury, John
1997
Role of fibroblast migration in collagen fiber formation during fetal and adult dermal wound healing. Zbl 0904.92024
Dale, Paul D.; Sherratt, Jonathan A.; Maini, Philip K.
1997
Vegetation patterns and desertification waves in semi-arid environments: mathematical models based on local facilitation in plants. Zbl 1395.35122
Sherratt, Jonathan A.; Synodinos, Alexios D.
2012
Mathematical modelling of juxtacrine patterning. Zbl 1323.92032
Wearing, H. J.; Owen, M. R.; Sherratt, J. A.
2000
Periodic travelling wave selection by Dirichlet boundary conditions in oscillatory reaction-diffusion systems. Zbl 1036.35093
Sherratt, Jonathan A.
2003
Diffusion-driven instability in oscillating environments. Zbl 0847.35066
Sherratt, Jonathan A.
1995
When does colonisation of a semi-arid hillslope generate vegetation patterns? Zbl 1343.92551
Sherratt, Jonathan A.
2016
Simpel modelling of extracellular matrix alignment in dermal wound healing. I: Cell flux induced alignment. Zbl 0912.92017
Olsen, Luke; Maini, Philip K.; Sherratt, Jonathan A.; Marchant, Ben
1998
Periodic traveling waves in integrodifferential equations for nonlocal dispersal. Zbl 06388268
Sherratt, Jonathan A.
2014
Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator-prey model. Zbl 1285.34049
Taylor, Rachel A.; Sherratt, Jonathan A.; White, Andrew
2013
How does tidal flow affect pattern formation in mussel beds? Zbl 1344.92189
Sherratt, Jonathan A.; Mackenzie, Julia J.
2016
Travelling waves in wound healing. Zbl 1003.92512
Dale, Paul D.; Olsen, Luke; Maini, Philip K.; Sherratt, Jonathan A.
1995
The effects of obstacle size on periodic travelling waves in oscillatory reaction-diffusion equations. Zbl 1154.35059
Smith, Matthew J.; Sherratt, Jonathan A.; Armstrong, Nicola J.
2008
Irregular wakes in reaction-diffusion waves. Zbl 0812.35062
Sherratt, Jonathan A.
1994
Periodic travelling waves in a family of deterministic cellular automata. Zbl 0888.35051
Sherratt, Jonathan A.
1996
Cells behaving badly: A theoretical model for the fas/FasL system in tumour immunology. Zbl 1014.92022
Webb, Steven D.; Sherratt, Jonathan A.; Fish, Reginald G.
2002
On the persistence of spatiotemporal oscillations generated by invasion. Zbl 0939.35091
Kay, Alison L.; Sherratt, Jonathan A.
1999
The speed of corneal epithelial wound healing. Zbl 0791.92013
Dale, P. D.; Sherratt, J. A.; Maini, P. K.
1994
Spatial noise stabilizes periodic wave patterns in oscillatory systems on finite domains. Zbl 1016.92002
Kay, Alison L.; Sherratt, Jonathan A.
2000
Mathematical models of wound healing in embryonic and adult epidermis. Zbl 0767.92013
Sherratt, Jonathan A.; Martin, Paul; Murray, J. D.; Lewis, Julian
1992
Keratinocyte growth factor signalling: A mathematical model of dermal-epidermal interaction in epidermal wound healing. Zbl 0963.92026
Wearning, Helen J.; Sherratt, Jonathan A.
2000
Oscillatory reaction-diffusion equations with temporally varying parameters. Zbl 1049.35104
Webb, S. D.; Sherratt, J. A.
2004
Cellular growth control and travelling waves of cancer. Zbl 0811.92018
Sherratt, Jonathan A.
1993
Macrophage dynamics in diabetic wound dealing. Zbl 1334.92213
Waugh, Helen V.; Sherratt, Jonathan A.
2006
A mathematical model for spatially varying extracellular matrix alignment. Zbl 1012.92019
Dallon, John C.; Sherratt, Jonathan A.
2000
Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair. Zbl 0966.92009
Dallon, John; Sherratt, Jonathan; Maini, Philip; Ferguson, Mark
2000
Stress-induced alignment of actin filaments and the mechanics of cytogel. Zbl 0765.92008
Sherratt, Jonathan A.; Lewis, Julian
1993
Patterns of sources and sinks in the complex Ginzburg-Landau equation with zero linear dispersion. Zbl 1197.35280
Sherratt, Jonathan A.; Smith, Matthew J.; Rademacher, Jens D. M.
2010
A comparison of two numerical methods for oscillatory reaction-diffusion systems. Zbl 0883.65071
Sherratt, J. A.
1997
A mechanochemical model for normal and abnormal dermal wound repair. Zbl 0892.92010
Olsen, Luke; Maini, Philip; Sherratt, Jonathan
1997
Mathematical models for cell-matrix interactions during dermal wound healing. Zbl 1041.92011
Maini, P. K.; Olsen, L.; Sherratt, J. A.
2002
Spatio-temporal models of lymphangiogenesis in wound healing. Zbl 1352.92016
Bianchi, Arianna; Painter, Kevin J.; Sherratt, Jonathan A.
2016
The amplitude of periodic plane waves depends on initial conditions in a variety of $$\lambda$$-$$\omega$$ systems. Zbl 0795.35049
Sherratt, Jonathan A.
1993
Wound healing in the corneal epithelium: Biological mechanisms and mathematical models. Zbl 0900.92080
Gaffney, Eamonn A.; Maini, Philip K.; Sherratt, Jonathan A.; Dale, Paul D.
1997
A comparison of periodic travelling wave generation by Robin and Dirichlet boundary conditions in oscillatory reaction-diffusion equations. Zbl 1184.35269
Sherratt, Jonathan A.
2008
Generation of periodic travelling waves in cyclic populations by hostile boundaries. Zbl 1348.92131
Sherratt, Jonathan A.
2013
Metastability as a coexistence mechanism in a model for dryland vegetation patterns. Zbl 1417.92209
Eigentler, Lukas; Sherratt, Jonathan A.
2019
The effects of density-dependent dispersal on the spatiotemporal dynamics of cyclic populations. Zbl 1400.92445
Smith, Matthew J.; Sherratt, Jonathan A.; Lambin, Xavier
2008
Spatial self-organisation enables species coexistence in a model for savanna ecosystems. Zbl 1429.92140
Eigentler, L.; Sherratt, J. A.
2020
Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts. Zbl 1422.92183
Bennett, Jamie J. R.; Sherratt, Jonathan A.
2019
Nonlinear analysis of juxtacrine patterns. Zbl 0992.92003
Wearing, Helen J.; Sherratt, Jonathan A.
2001
Spatiotemporal patterning in models of juxtacrine intercellular signalling with feedback. Zbl 1022.92002
Monk, Nicholas A. M.; Sherratt, Jonathan A.; Owen, Markus R.
2000
Spatial self-organisation enables species coexistence in a model for savanna ecosystems. Zbl 1429.92140
Eigentler, L.; Sherratt, J. A.
2020
An integrodifference model for vegetation patterns in semi-arid environments with seasonality. Zbl 1454.37088
Eigentler, Lukas; Sherratt, Jonathan A.
2020
Metastability as a coexistence mechanism in a model for dryland vegetation patterns. Zbl 1417.92209
Eigentler, Lukas; Sherratt, Jonathan A.
2019
Long-distance seed dispersal affects the resilience of banded vegetation patterns in semi-deserts. Zbl 1422.92183
Bennett, Jamie J. R.; Sherratt, Jonathan A.
2019
How do dispersal rates affect the transition from periodic to irregular spatio-temporal oscillations in invasive predator-prey systems? Zbl 1411.92242
Bennett, Jamie J. R.; Sherratt, Jonathan A.
2019
Analysis of a model for banded vegetation patterns in semi-arid environments with nonlocal dispersal. Zbl 1453.35025
Eigentler, Lukas; Sherratt, Jonathan A.
2018
Periodic traveling waves generated by invasion in cyclic predator-prey systems: the effect of unequal dispersal. Zbl 1387.35089
Bennett, Jamie J. R.; Sherratt, Jonathan A.
2017
Invasion generates periodic traveling waves (wavetrains) in predator-prey models with nonlocal dispersal. Zbl 1382.35323
Sherratt, Jonathan A.
2016
When does colonisation of a semi-arid hillslope generate vegetation patterns? Zbl 1343.92551
Sherratt, Jonathan A.
2016
How does tidal flow affect pattern formation in mussel beds? Zbl 1344.92189
Sherratt, Jonathan A.; Mackenzie, Julia J.
2016
Spatio-temporal models of lymphangiogenesis in wound healing. Zbl 1352.92016
Bianchi, Arianna; Painter, Kevin J.; Sherratt, Jonathan A.
2016
Using numerical bifurcation analysis to study pattern formation in mussel beds. Zbl 1384.92014
Sherratt, J. A.
2016
A nonlocal model for contact attraction and repulsion in heterogeneous cell populations. Zbl 1335.92026
Painter, K. J.; Bloomfield, J. M.; Sherratt, J. A.; Gerisch, A.
2015
A mathematical model for lymphangiogenesis in normal and diabetic wounds. Zbl 1343.92062
Bianchi, Arianna; Painter, Kevin J.; Sherratt, Jonathan A.
2015
A mathematical biologist’s guide to absolute and convective instability. Zbl 1283.92007
Sherratt, Jonathan A.; Dagbovie, Ayawoa S.; Hilker, Frank M.
2014
Absolute stability and dynamical stabilisation in predator-prey systems. Zbl 1284.92109
Dagbovie, Ayawoa S.; Sherratt, Jonathan A.
2014
Periodic traveling waves in integrodifferential equations for nonlocal dispersal. Zbl 06388268
Sherratt, Jonathan A.
2014
Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments. V: The transition from patterns to desert. Zbl 1320.92078
Sherratt, Jonathan A.
2013
Pattern solutions of the Klausmeier model for banded vegetation in semiarid environments. IV: Slowly moving patterns and their stability. Zbl 1321.92083
Sherratt, Jonathan A.
2013
Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. III: The transition between homoclinic solutions. Zbl 1261.35144
Sherratt, Jonathan A.
2013
Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations. Zbl 1271.65132
Sherratt, Jonathan A.
2013
Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator-prey model. Zbl 1285.34049
Taylor, Rachel A.; Sherratt, Jonathan A.; White, Andrew
2013
Generation of periodic travelling waves in cyclic populations by hostile boundaries. Zbl 1348.92131
Sherratt, Jonathan A.
2013
Stability switches in a host-pathogen model as the length of a time delay increases. Zbl 1301.92066
Reynolds, Jennifer J. H.; Sherratt, Jonathan A.; White, Andrew
2013
The mean values of the Weierstrass elliptic function $$\wp$$: theory and application. Zbl 1293.33023
Sherratt, Jonathan A.; Brezhnev, Yurii V.
2013
Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations. Zbl 1244.65155
Sherratt, Jonathan A.
2012
Vegetation patterns and desertification waves in semi-arid environments: mathematical models based on local facilitation in plants. Zbl 1395.35122
Sherratt, Jonathan A.; Synodinos, Alexios D.
2012
Turing patterns in deserts. Zbl 1358.92030
Sherratt, Jonathan A.
2012
Transition to spatiotemporal chaos via stationary branching shocks and holes. Zbl 1253.35172
Sherratt, Jonathan A.; Smith, Matthew J.
2012
Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. II: Patterns with the largest possible propagation speeds. Zbl 1239.92085
Sherratt, Jonathan A.
2011
How does cellular contact affect differentiation mediated pattern formation? Zbl 1225.92013
Bloomfield, J. M.; Painter, K. J.; Sherratt, J. A.
2011
The population dynamical consequences of density-dependent prophylaxis. Zbl 1397.92675
Reynolds, Jennifer J. H.; White, Andrew; Sherratt, Jonathan A.; Boots, Mike
2011
Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. I. Zbl 1197.92047
Sherratt, Jonathan A.
2010
The impact of adhesion on cellular invasion processes in cancer and development. Zbl 1406.92156
Painter, Kevin J.; Armstrong, Nicola J.; Sherratt, Jonathan A.
2010
On the form of smooth-front travelling waves in a reaction-diffusion equation with degenerate nonlinear diffusion. Zbl 1202.35050
Sherratt, J. A.
2010
Patterns of sources and sinks in the complex Ginzburg-Landau equation with zero linear dispersion. Zbl 1197.35280
Sherratt, Jonathan A.; Smith, Matthew J.; Rademacher, Jens D. M.
2010
Boundedness of solutions of a non-local reaction-diffusion model for adhesion in cell aggregation and cancer invasion. Zbl 1194.35219
Sherratt, Jonathan A.; Gourley, Stephen A.; Armstrong, Nicola J.; Painter, Kevin J.
2009
Adding adhesion to a chemical signaling model for somite formation. Zbl 1169.92008
Armstrong, Nicola J.; Painter, Kevin J.; Sherratt, Jonathan A.
2009
Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion. Zbl 1203.37062
Sherratt, Jonathan A.; Smith, Matthew J.; Rademacher, Jens D. M.
2009
Absolute stability of wavetrains can explain spatiotemporal dynamics in reaction-diffusion systems of lambda-omega type. Zbl 1183.35032
Smith, Matthew J.; Rademacher, Jens D. M.; Sherratt, Jonathan A.
2009
The effects of obstacle size on periodic travelling waves in oscillatory reaction-diffusion equations. Zbl 1154.35059
Smith, Matthew J.; Sherratt, Jonathan A.; Armstrong, Nicola J.
2008
A comparison of periodic travelling wave generation by Robin and Dirichlet boundary conditions in oscillatory reaction-diffusion equations. Zbl 1184.35269
Sherratt, Jonathan A.
2008
The effects of density-dependent dispersal on the spatiotemporal dynamics of cyclic populations. Zbl 1400.92445
Smith, Matthew J.; Sherratt, Jonathan A.; Lambin, Xavier
2008
Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments. Zbl 1118.92064
Sherratt, Jonathan A.; Lord, Gabriel J.
2007
The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems. Zbl 1361.34040
Smith, Matthew J.; Sherratt, Jonathan A.
2007
A continuum approach to modelling cell-cell adhesion. Zbl 1447.92113
Armstrong, Nicola J.; Painter, Kevin J.; Sherratt, Jonathan A.
2006
Macrophage dynamics in diabetic wound dealing. Zbl 1334.92213
Waugh, Helen V.; Sherratt, Jonathan A.
2006
An analysis of vegetation stripe formation in semi-arid landscapes. Zbl 1068.92047
Sherratt, Jonathan A.
2005
Oscillatory reaction-diffusion equations with temporally varying parameters. Zbl 1049.35104
Webb, S. D.; Sherratt, J. A.
2004
Modelling the movement of interacting cell populations. Zbl 1464.92050
Painter, Kevin J.; Sherratt, Jonathan A.
2003
Periodic travelling wave selection by Dirichlet boundary conditions in oscillatory reaction-diffusion systems. Zbl 1036.35093
Sherratt, Jonathan A.
2003
A perturbation problem arising from the modelling of soluble Fas ligand in tumour immunology. Zbl 1022.92014
Webb, S. D.; Sherratt, J. A.
2003
Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Zbl 1334.92106
McDougall, S. R.; Anderson, A. R. A.; Chaplain, M. A. J.; Sherratt, J. A.
2002
Lipoprotein oxidation and its significance for atherosclerosis: a mathematical approach. Zbl 1334.92131
Cobbold, C. A.; Sherratt, J. A.; Maxwell, S. R. J.
2002
Cells behaving badly: A theoretical model for the fas/FasL system in tumour immunology. Zbl 1014.92022
Webb, Steven D.; Sherratt, Jonathan A.; Fish, Reginald G.
2002
Mathematical models for cell-matrix interactions during dermal wound healing. Zbl 1041.92011
Maini, P. K.; Olsen, L.; Sherratt, J. A.
2002
Modelling blood flow regulation by nitric oxide in psoriatic plaques. Zbl 1334.92107
Sherratt, Jonathan A.; Weller, Richard; Savill, Nicholas J.
2002
A new mathematical model for avascular tumour growth. Zbl 0990.92021
Sherratt, Jonathan A.; Chaplain, Mark A. J.
2001
Travelling wave solutions to a haptotaxis-dominated model of malignant invasion. Zbl 0985.92012
Marchant, B. P.; Norbury, J.; Sherratt, J. A.
2001
Comparison theorems and variable speed waves for a scalar reaction-diffusion equation. Zbl 0996.35034
Kay, Alison L.; Sherratt, Jonathan A.; McLeod, J. B.
2001
Nonlinear analysis of juxtacrine patterns. Zbl 0992.92003
Wearing, Helen J.; Sherratt, Jonathan A.
2001
Wavefront propagation in a competition equation with a new motility term modelling contact inhibition between cell populations. Zbl 1005.76098
Sherratt, Jonathan A.
2000
Traveling wave solutions of a mathematical model for tumor encapsulation. Zbl 1012.92018
Sherratt, Jonathan A.
2000
Mathematical modelling of juxtacrine patterning. Zbl 1323.92032
Wearing, H. J.; Owen, M. R.; Sherratt, J. A.
2000
Spatial noise stabilizes periodic wave patterns in oscillatory systems on finite domains. Zbl 1016.92002
Kay, Alison L.; Sherratt, Jonathan A.
2000
Keratinocyte growth factor signalling: A mathematical model of dermal-epidermal interaction in epidermal wound healing. Zbl 0963.92026
Wearning, Helen J.; Sherratt, Jonathan A.
2000
A mathematical model for spatially varying extracellular matrix alignment. Zbl 1012.92019
Dallon, John C.; Sherratt, Jonathan A.
2000
Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair. Zbl 0966.92009
Dallon, John; Sherratt, Jonathan; Maini, Philip; Ferguson, Mark
2000
Spatiotemporal patterning in models of juxtacrine intercellular signalling with feedback. Zbl 1022.92002
Monk, Nicholas A. M.; Sherratt, Jonathan A.; Owen, Markus R.
2000
A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion. Zbl 1001.92523
Perumpanai, Abbey J.; Sherratt, Jonathan; Norbury, John; Byrne, Helen M.
1999
Mathematical modelling of macrophage dynamics in tumours. Zbl 0932.92019
Owen, Markus R.; Sherratt, Jonathan A.
1999
Mathematical modelling of anisotropy in fibrous connective tissue. Zbl 0953.92011
Olsen, Luke; Maini, Philip K.; Sherratt, Jonathan A.; Dallon, John
1999
On the persistence of spatiotemporal oscillations generated by invasion. Zbl 0939.35091
Kay, Alison L.; Sherratt, Jonathan A.
1999
On the transition from initial data to travelling waves in the Fisher-KPP equation. Zbl 0912.35084
Sherratt, Jonathan A.
1998
Modelling the macrophage invasion of tumours: Effects on growth and composition. Zbl 0909.92022
Owen, Markus R.; Sherratt, Jonathan A.
1998
Unravelling the Turing bifurcation using spatially varying diffusion coefficients. Zbl 0919.92006
Benson, Debbie L.; Maini, Philip K.; Sherratt, Jonathan A.
1998
Invading wave fronts and their oscillatory wakes are linked by a modulated travelling phase resetting wave. Zbl 0940.35111
Sherratt, Jonathan A.
1998
Spatially varying equilibria of mechanical models: Application to dermal wound contraction. Zbl 0888.92021
Olsen, Luke; Maini, Philip K.; Sherratt, Jonathan A.
1998
Mathematical modelling of juxtacrine cell signalling. Zbl 0940.92009
Owen, Markus R.; Sherratt, Jonathan A.
1998
A mathematical model for fibroblast and collagen orientation. Zbl 0909.92014
Dallon, John C.; Sherratt, Jonathan A.
1998
Simpel modelling of extracellular matrix alignment in dermal wound healing. I: Cell flux induced alignment. Zbl 0912.92017
Olsen, Luke; Maini, Philip K.; Sherratt, Jonathan A.; Marchant, Ben
1998
A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis. Zbl 0891.92016
Olsen, Luke; Sherratt, Jonathan A.; Maini, Philip K.; Arnold, Frank
1997
On the propagation of calcium waves in an inhomogeneous medium. Zbl 0866.35128
Sneyd, James; Sherratt, Jonathan
1997
Mathematical modelling of capsule formation and multinodularity in benign tumour growth. Zbl 0910.92017
Perumpanani, Abbey J.; Sherratt, Jonathan A.; Norbury, John
1997
Role of fibroblast migration in collagen fiber formation during fetal and adult dermal wound healing. Zbl 0904.92024
Dale, Paul D.; Sherratt, Jonathan A.; Maini, Philip K.
1997
A comparison of two numerical methods for oscillatory reaction-diffusion systems. Zbl 0883.65071
Sherratt, J. A.
1997
A mechanochemical model for normal and abnormal dermal wound repair. Zbl 0892.92010
Olsen, Luke; Maini, Philip; Sherratt, Jonathan
1997
Wound healing in the corneal epithelium: Biological mechanisms and mathematical models. Zbl 0900.92080
Gaffney, Eamonn A.; Maini, Philip K.; Sherratt, Jonathan A.; Dale, Paul D.
1997
Algebraic decay and variable speeds in wavefront solutions of a scalar reaction-diffusion equation. Zbl 0858.35062
Sherratt, Jonathan A.; Marchant, Ben P.
1996
Nonsharp travelling wave fronts in the Fisher equation with degenerate nonlinear diffusion. Zbl 0903.35026
Sherratt, J. A.; Marchant, B. P.
1996
A mathematical model for fibro-proliferative wound healing disorders. Zbl 0865.92010
Olsen, Luke; Sherratt, Jonathan A.; Maini, Philip K.
1996
Periodic travelling waves in a family of deterministic cellular automata. Zbl 0888.35051
Sherratt, Jonathan A.
1996
Oscillatory and chaotic wakes behind moving boundaries in reaction-diffusion systems. Zbl 0877.35058
Sherratt, Jonathan A.
1996
Periodic waves in reaction-diffusion models of oscillatory biological systems. Zbl 1003.92508
Sherratt, Jonathan A.
1996
Ecological chaos in the wake of invasion. Zbl 0819.92024
Sherratt, Jonathan; Lewis, Mark A.; Fowler, Andrew C.
1995
Cellular pattern formation during Dictyostelium aggregation. Zbl 0888.92005
Höfer, Thomas; Sherratt, Jonathan A.; Maini, Philip K.
1995
Phase differences in reaction-diffusion-advection systems and applications to morphogenesis. Zbl 0843.35041
Perumpanani, Abbey J.; Sherratt, Jonathan A.; Maini, Philip K.
1995
Turing bifurcations with a temporally varying diffusion coefficient. Zbl 0812.92024
Sherratt, Jonathan A.
1995
Unstable wavetrains and chaotic wakes in reaction-diffusion systems of $$\lambda-\omega$$ type. Zbl 0900.35194
Sherratt, Jonathan A.
1995
Diffusion-driven instability in oscillating environments. Zbl 0847.35066
Sherratt, Jonathan A.
1995
...and 18 more Documents
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Cited by 1,444 Authors

 60 Sherratt, Jonathan A. 31 Maini, Philip Kumar 27 Chaplain, Mark A. J. 25 Simpson, Matthew J. 22 Byrne, Helen Mary 20 Painter, Kevin J. 18 Petrovskii, Sergei V. 12 Carrillo de la Plata, José Antonio 11 Malchow, Horst 11 Preziosi, Luigi 10 Banerjee, Malay 9 Gerisch, Alf 9 McCue, Scott William 9 Mcelwain, D. L. Sean 8 Baker, Ruth Elizabeth 8 Doelman, Arjen 8 Eftimie, Raluca 8 Kolokolnikov, Theodore 8 Landman, Kerry A. 8 Perthame, Benoît 8 van Heijster, Peter 8 Wei, Juncheng 7 Krause, Andrew L. 7 Lorenzi, Tommaso 7 Lutscher, Frithjof 7 Myerscough, Mary R. 7 Owen, Markus Roger 6 Anderson, Alexander R. A. 6 Bhattacharyya, Rakhi 6 Gaffney, Eamonn A. 6 Hillen, Thomas 6 Jin, Zhen 6 Kumar Upadhyay, Ranjit 6 Lowengrub, John Samuel 6 McDougall, Steven R. 6 Mukhopadhyay, Banibrata 6 Ou, Chunhua 6 Scianna, Marco 6 Sun, Guiquan 6 Vermolen, Fred J. 6 Winkler, Michael 6 Winter, Matthias 5 Bellomo, Nicola 5 Colombi, Annachiara 5 Deutsch, Andreas 5 Friedman, Avner 5 Garvie, Marcus R. 5 Herrero, Miguel Ángel 5 King, John Robert 5 Li, Bailian 5 Long, Quan 5 Mansour, Mahmoud Bakheet A. 5 Olsen, Luke 5 Popović, Nikola 5 Scheel, Arnd 5 Schmidtchen, Markus 5 Shi, Junping 5 Tian, Canrong 5 Wei, Junjie 5 Xu, Shixiong 5 Zhang, Guohong 4 Bennett, Jamie J. R. 4 Buenzli, Pascal R. 4 Cai, Yan 4 Cristini, Vittorio 4 Currò, Carmela 4 Eigentler, Lukas 4 Frieboes, Hermann B. 4 Giannino, Francesco 4 Gourley, Stephen A. 4 Green, J. Edward F. 4 Harley, Kristen E. 4 Hilker, Frank M. 4 Javierre, E. 4 Klika, Václav 4 Kuang, Yang 4 Marangell, Robert 4 Mimura, Masayasu 4 Morozov, Andrew Yu. 4 Murakawa, Hideki 4 Murphy, Ryan J. 4 Norbury, John W. 4 Pal, Swadesh 4 Pettet, Graeme John 4 Plaza, Ramón G. 4 Ptashnyk, Mariya 4 Rademacher, Jens Diederich Michael 4 Sandstede, Björn 4 Smith, Matthew J. 4 Trucu, Dumitru 4 Tzou, Justin C. 4 Valenti, Giovanna 4 van Gorder, Robert Ashton 4 Volpert, Vitaly A. 4 Wang, Zhian 4 Waters, Sarah Louise 4 Webb, Steven D. 3 Alarcón, Tomás 3 Allena, Rachele 3 Baek, Hunki ...and 1,344 more Authors
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Cited in 149 Serials

 97 Journal of Theoretical Biology 87 Bulletin of Mathematical Biology 62 Journal of Mathematical Biology 38 Mathematical Biosciences 32 Mathematical and Computer Modelling 29 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 24 Applied Mathematics and Computation 24 Physica D 18 SIAM Journal on Applied Mathematics 18 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 15 Journal of Differential Equations 15 Applied Mathematics Letters 14 SIAM Journal on Applied Dynamical Systems 13 Computers & Mathematics with Applications 12 Journal of Mathematical Analysis and Applications 11 Chaos 11 Nonlinear Analysis. Real World Applications 11 Discrete and Continuous Dynamical Systems. Series B 10 Applied Mathematical Modelling 10 Mathematical Biosciences and Engineering 10 Mathematical Modelling of Natural Phenomena 9 Nonlinearity 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 9 Theoretical Population Biology 8 Mathematics and Computers in Simulation 8 Computational & Mathematical Methods in Medicine 7 Journal of Dynamics and Differential Equations 7 Journal of Nonlinear Science 7 Communications in Nonlinear Science and Numerical Simulation 6 Journal of Computational Physics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 European Journal of Applied Mathematics 6 Discrete and Continuous Dynamical Systems 6 Journal of Mathematical Chemistry 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 6 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 5 Journal of Computational and Applied Mathematics 4 Physica A 4 Dynamics and Stability of Systems 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Journal of Difference Equations and Applications 4 Journal of Biological Systems 4 Journal of Applied Mathematics 4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Chaos, Solitons and Fractals 3 Numerische Mathematik 3 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 3 Applied Mathematics and Mechanics. (English Edition) 3 Acta Applicandae Mathematicae 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 SIAM Journal on Mathematical Analysis 3 Computational and Applied Mathematics 3 Abstract and Applied Analysis 3 Journal of Biological Dynamics 3 Discrete and Continuous Dynamical Systems. Series S 3 Kinetic and Related Models 3 International Journal of Biomathematics 2 Applicable Analysis 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal of Engineering Science 2 International Journal of Systems Science 2 Journal of Mathematical Physics 2 Wave Motion 2 Ricerche di Matematica 2 Studies in Applied Mathematics 2 Transactions of the American Mathematical Society 2 Applied Numerical Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Scientific Computing 2 International Journal of Computer Mathematics 2 Proceedings of the National Academy of Sciences of the United States of America 2 Journal of Theoretical Medicine 2 Discrete Dynamics in Nature and Society 2 Interfaces and Free Boundaries 2 The ANZIAM Journal 2 Archives of Computational Methods in Engineering 2 Dynamical Systems 2 Communications on Pure and Applied Analysis 2 Multiscale Modeling & Simulation 2 Acta Mechanica Sinica 2 Communications in Applied and Industrial Mathematics 1 Acta Mechanica 1 Archive for Rational Mechanics and Analysis 1 International Journal of Solids and Structures 1 Inverse Problems 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Journal of the Franklin Institute 1 Journal of the Mechanics and Physics of Solids 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 Physics Letters. A 1 Physics Reports 1 Ukrainian Mathematical Journal 1 Journal of Geometry and Physics 1 BIT 1 Calcolo 1 Journal of Applied Probability 1 Kyungpook Mathematical Journal 1 Meccanica ...and 49 more Serials
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Cited in 32 Fields

 691 Biology and other natural sciences (92-XX) 564 Partial differential equations (35-XX) 133 Numerical analysis (65-XX) 81 Dynamical systems and ergodic theory (37-XX) 79 Ordinary differential equations (34-XX) 32 Fluid mechanics (76-XX) 22 Probability theory and stochastic processes (60-XX) 19 Mechanics of deformable solids (74-XX) 18 Systems theory; control (93-XX) 12 Integral equations (45-XX) 11 Statistics (62-XX) 10 Difference and functional equations (39-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 10 Computer science (68-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 Operator theory (47-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Geophysics (86-XX) 3 Real functions (26-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 1 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX)