Paquin-Lefebvre, F.; Iyaniwura, S.; Ward, M. J. Asymptotics of the principal eigenvalue of the Laplacian in 2D periodic domains with small traps. (English) Zbl 1505.35022 Eur. J. Appl. Math. 33, No. 4, 646-673 (2022). MSC: 35B25 35C20 35J25 35P15 PDFBibTeX XMLCite \textit{F. Paquin-Lefebvre} et al., Eur. J. Appl. Math. 33, No. 4, 646--673 (2022; Zbl 1505.35022) Full Text: DOI
Kolokolnikov, Theodore; Ward, Michael A ring of spikes in a Schnakenberg model. (English) Zbl 1498.35026 Physica D 441, Article ID 133521, 13 p. (2022). MSC: 35B25 35K51 35K57 PDFBibTeX XMLCite \textit{T. Kolokolnikov} and \textit{M. Ward}, Physica D 441, Article ID 133521, 13 p. (2022; Zbl 1498.35026) Full Text: DOI
Wong, Tony; Ward, Michael J. Dynamics of patchy vegetation patterns in the two-dimensional generalized Klausmeier model. (English) Zbl 1498.35057 Discrete Contin. Dyn. Syst., Ser. S 15, No. 9, 2747-2793 (2022). MSC: 35B36 35B25 35B32 35K57 35Q92 PDFBibTeX XMLCite \textit{T. Wong} and \textit{M. J. Ward}, Discrete Contin. Dyn. Syst., Ser. S 15, No. 9, 2747--2793 (2022; Zbl 1498.35057) Full Text: DOI
Ridgway, Wesley; Ward, Michael J.; Wetton, Brian T. Quorum-sensing induced transitions between bistable steady-states for a cell-bulk ODE-PDE model with lux intracellular kinetics. (English) Zbl 1483.35289 J. Math. Biol. 84, No. 1-2, Paper No. 5, 59 p. (2022). MSC: 35Q92 35B25 35P30 92C05 92D25 92C37 93C15 93C20 PDFBibTeX XMLCite \textit{W. Ridgway} et al., J. Math. Biol. 84, No. 1--2, Paper No. 5, 59 p. (2022; Zbl 1483.35289) Full Text: DOI
Iyaniwura, Sarafa A.; Gou, Jia; Ward, Michael J. Synchronous oscillations for a coupled cell-bulk ODE-PDE model with localized cells on \({\mathbb{R}}^2\). (English) Zbl 1498.35550 J. Eng. Math. 127, Paper No. 18, 25 p. (2021). MSC: 35Q92 92C37 92B25 92C15 92C05 35B32 35B05 35B35 PDFBibTeX XMLCite \textit{S. A. Iyaniwura} et al., J. Eng. Math. 127, Paper No. 18, 25 p. (2021; Zbl 1498.35550) Full Text: DOI
Iyaniwura, Sarafa A.; Ward, Michael J. Localised signalling compartments in 2D coupled by a bulk diffusion field: quorum sensing and synchronous oscillations in the well-mixed limit. (English) Zbl 1479.35051 Eur. J. Appl. Math. 32, No. 5, 1001-1031 (2021). MSC: 35B25 35B32 35B36 35K20 92B25 PDFBibTeX XMLCite \textit{S. A. Iyaniwura} and \textit{M. J. Ward}, Eur. J. Appl. Math. 32, No. 5, 1001--1031 (2021; Zbl 1479.35051) Full Text: DOI arXiv
Iyaniwura, Sarafa; Wong, Tony; Ward, Michael J.; Macdonald, Colin B. Simulation and optimization of mean first passage time problems in 2-d using numerical embedded methods and perturbation theory. (English) Zbl 1471.65103 Multiscale Model. Simul. 19, No. 3, 1367-1393 (2021). MSC: 65M06 65N06 35C20 35K05 35J05 PDFBibTeX XMLCite \textit{S. Iyaniwura} et al., Multiscale Model. Simul. 19, No. 3, 1367--1393 (2021; Zbl 1471.65103) Full Text: DOI arXiv
Iyaniwura, S.; Ward, M. J. Asymptotic analysis for the mean first passage time in finite or spatially periodic 2D domains with a cluster of small traps. (English) Zbl 1470.35029 ANZIAM J. 63, No. 1, 1-22 (2021). MSC: 35B25 35C20 35J05 35J08 PDFBibTeX XMLCite \textit{S. Iyaniwura} and \textit{M. J. Ward}, ANZIAM J. 63, No. 1, 1--22 (2021; Zbl 1470.35029) Full Text: DOI
Iyaniwura, Sarafa A.; Wong, Tony; Macdonald, Colin B.; Ward, Michael J. Optimization of the mean first passage time in near-disk and elliptical domains in 2-D with small absorbing traps. (English) Zbl 1470.35028 SIAM Rev. 63, No. 3, 525-555 (2021). MSC: 35B25 35C20 35P15 35J05 35J08 35Q93 PDFBibTeX XMLCite \textit{S. A. Iyaniwura} et al., SIAM Rev. 63, No. 3, 525--555 (2021; Zbl 1470.35028) Full Text: DOI arXiv
Gomez, Daniel; Ward, Michael J.; Wei, Juncheng An asymptotic analysis of localized three-dimensional spot patterns for the Gierer-Meinhardt model: existence, linear stability, and slow dynamics. (English) Zbl 1462.35031 SIAM J. Appl. Math. 81, No. 2, 378-406 (2021). MSC: 35B25 35K57 35B35 35B36 35B40 35C20 PDFBibTeX XMLCite \textit{D. Gomez} et al., SIAM J. Appl. Math. 81, No. 2, 378--406 (2021; Zbl 1462.35031) Full Text: DOI arXiv
Iyaniwura, Sarafa A.; Ward, Michael J. Synchrony and oscillatory dynamics for a 2-d PDE-ODE model of diffusion-mediated communication between small signaling compartments. (English) Zbl 1462.35227 SIAM J. Appl. Dyn. Syst. 20, No. 1, 438-499 (2021). MSC: 35P30 35B32 34E15 92C15 92C05 PDFBibTeX XMLCite \textit{S. A. Iyaniwura} and \textit{M. J. Ward}, SIAM J. Appl. Dyn. Syst. 20, No. 1, 438--499 (2021; Zbl 1462.35227) Full Text: DOI arXiv
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J. Competition instabilities of spike patterns for the 1D Gierer-Meinhardt and Schnakenberg models are subcritical. (English) Zbl 1456.35013 Nonlinearity 34, No. 1, 273-312 (2021). MSC: 35B25 35B32 35B35 35B36 35K57 92C15 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Nonlinearity 34, No. 1, 273--312 (2021; Zbl 1456.35013) Full Text: DOI
Buttenschoen, Andreas; Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng Cops-on-the-dots: the linear stability of crime hotspots for a 1-D reaction-diffusion model of urban crime. (English) Zbl 1504.35031 Eur. J. Appl. Math. 31, No. 5, 871-917 (2020). MSC: 35B25 35B32 35B35 35K51 35K57 PDFBibTeX XMLCite \textit{A. Buttenschoen} et al., Eur. J. Appl. Math. 31, No. 5, 871--917 (2020; Zbl 1504.35031) Full Text: DOI
David, Jummy F.; Iyaniwura, Sarafa A.; Ward, Michael J.; Brauer, Fred A novel approach to modelling the spatial spread of airborne diseases: an epidemic model with indirect transmission. (English) Zbl 1467.92186 Math. Biosci. Eng. 17, No. 4, 3294-3328 (2020). MSC: 92D30 34C60 35Q92 PDFBibTeX XMLCite \textit{J. F. David} et al., Math. Biosci. Eng. 17, No. 4, 3294--3328 (2020; Zbl 1467.92186) Full Text: DOI
Wong, Tony; Ward, Michael J. Weakly nonlinear analysis of peanut-shaped deformations for localized spots of singularly perturbed reaction-diffusion systems. (English) Zbl 1472.35026 SIAM J. Appl. Dyn. Syst. 19, No. 3, 2030-2058 (2020). MSC: 35B25 35B32 35B36 35B60 35K51 35K57 37G05 65P30 PDFBibTeX XMLCite \textit{T. Wong} and \textit{M. J. Ward}, SIAM J. Appl. Dyn. Syst. 19, No. 3, 2030--2058 (2020; Zbl 1472.35026) Full Text: DOI arXiv
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J. Weakly nonlinear theory for oscillatory dynamics in a one-dimensional PDE-ODE model of membrane dynamics coupled by a bulk diffusion field. (English) Zbl 1446.37071 SIAM J. Appl. Math. 80, No. 3, 1520-1545 (2020). MSC: 37M20 65P30 35B36 35B35 34C15 74K15 70K55 70K50 PDFBibTeX XMLCite \textit{F. Paquin-Lefebvre} et al., SIAM J. Appl. Math. 80, No. 3, 1520--1545 (2020; Zbl 1446.37071) Full Text: DOI arXiv
Chang, Yifan; Tzou, J. C.; Ward, M. J.; Wei, J. C. Refined stability thresholds for localized spot patterns for the Brusselator model in \(\mathbb{R}^2\). (English) Zbl 1427.35107 Eur. J. Appl. Math. 30, No. 4, 791-828 (2019). MSC: 35K51 35K58 35B25 PDFBibTeX XMLCite \textit{Y. Chang} et al., Eur. J. Appl. Math. 30, No. 4, 791--828 (2019; Zbl 1427.35107) Full Text: DOI
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J. Pattern formation and oscillatory dynamics in a two-dimensional coupled bulk-surface reaction-diffusion system. (English) Zbl 1428.37071 SIAM J. Appl. Dyn. Syst. 18, No. 3, 1334-1390 (2019). MSC: 37L10 35K57 37M20 35B35 35B36 65P30 PDFBibTeX XMLCite \textit{F. Paquin-Lefebvre} et al., SIAM J. Appl. Dyn. Syst. 18, No. 3, 1334--1390 (2019; Zbl 1428.37071) Full Text: DOI arXiv
Gomez, Daniel; Ward, Michael J.; Wei, Juncheng The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model. (English) Zbl 1419.35107 SIAM J. Appl. Dyn. Syst. 18, No. 2, 729-768 (2019). Reviewer: Denise Huet (Nancy) MSC: 35K57 35A08 35B25 35B36 92C15 35Q92 PDFBibTeX XMLCite \textit{D. Gomez} et al., SIAM J. Appl. Dyn. Syst. 18, No. 2, 729--768 (2019; Zbl 1419.35107) Full Text: DOI arXiv
Kolokolnikov, Theodore; Ward, Michael; Tzou, Justin; Wei, Juncheng Stabilizing a homoclinic stripe. (English) Zbl 1425.35100 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2135, Article ID 20180110, 13 p. (2018). MSC: 35K57 35K51 35M33 35B25 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2135, Article ID 20180110, 13 p. (2018; Zbl 1425.35100) Full Text: DOI Link
Tse, Wang Hung; Ward, Michael J. Asynchronous instabilities of crime hotspots for a 1-D reaction-diffusion model of urban crime with focused police patrol. (English) Zbl 1397.35138 SIAM J. Appl. Dyn. Syst. 17, No. 3, 2018-2075 (2018). MSC: 35K57 35B25 35B32 35K51 91D99 PDFBibTeX XMLCite \textit{W. H. Tse} and \textit{M. J. Ward}, SIAM J. Appl. Dyn. Syst. 17, No. 3, 2018--2075 (2018; Zbl 1397.35138) Full Text: DOI
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng A time-delay in the activator kinetics enhances the stability of a spike solution to the Gierer-Meinhardt model. (English) Zbl 1395.37055 Discrete Contin. Dyn. Syst., Ser. B 23, No. 4, 1431-1458 (2018). MSC: 37N25 92E20 35K57 92C15 92C37 35Q92 PDFBibTeX XMLCite \textit{N. T. Fadai} et al., Discrete Contin. Dyn. Syst., Ser. B 23, No. 4, 1431--1458 (2018; Zbl 1395.37055) Full Text: DOI
Tzou, J. C.; Ward, M. J. The stability and slow dynamics of spot patterns in the 2D Brusselator model: the effect of open systems and heterogeneities. (English) Zbl 1392.35039 Physica D 373, 13-37 (2018). MSC: 35B36 92E20 35B40 PDFBibTeX XMLCite \textit{J. C. Tzou} and \textit{M. J. Ward}, Physica D 373, 13--37 (2018; Zbl 1392.35039) Full Text: DOI
Ward, M. J. Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems. (English) Zbl 1393.35106 Nonlinearity 31, No. 8, R189-R239 (2018). MSC: 35K57 35P05 35B25 35J05 PDFBibTeX XMLCite \textit{M. J. Ward}, Nonlinearity 31, No. 8, R189--R239 (2018; Zbl 1393.35106) Full Text: DOI Link
Tzou, J. C.; Ward, M. J.; Wei, J. C. Anomalous scaling of Hopf bifurcation thresholds for the stability of localized spot patterns for reaction-diffusion systems in two dimensions. (English) Zbl 1391.35225 SIAM J. Appl. Dyn. Syst. 17, No. 1, 982-1022 (2018). MSC: 35K57 35P05 35B25 PDFBibTeX XMLCite \textit{J. C. Tzou} et al., SIAM J. Appl. Dyn. Syst. 17, No. 1, 982--1022 (2018; Zbl 1391.35225) Full Text: DOI
Avitabile, Daniele; Breña-Medina, Victor F.; Ward, Michael J. Spot dynamics in a reaction-diffusion model of plant root hair initiation. (English) Zbl 1383.92048 SIAM J. Appl. Math. 78, No. 1, 291-319 (2018). MSC: 92C80 92C15 35K57 65N25 PDFBibTeX XMLCite \textit{D. Avitabile} et al., SIAM J. Appl. Math. 78, No. 1, 291--319 (2018; Zbl 1383.92048) Full Text: DOI arXiv
Rottschäfer, V.; Tzou, J. C.; Ward, M. J. Transition to blow-up in a reaction-diffusion model with localized spike solutions. (English) Zbl 1387.35338 Eur. J. Appl. Math. 28, No. 6, 1015-1055 (2017). MSC: 35K51 35K58 35B44 35B25 PDFBibTeX XMLCite \textit{V. Rottschäfer} et al., Eur. J. Appl. Math. 28, No. 6, 1015--1055 (2017; Zbl 1387.35338) Full Text: DOI
Gou, Jia; Chiang, Wei-Yin; Lai, Pik-Yin; Ward, Michael J.; Li, Yue-Xian A theory of synchrony by coupling through a diffusive chemical signal. (English) Zbl 1376.92020 Physica D 339, 1-17 (2017). MSC: 92C45 92B25 34C60 PDFBibTeX XMLCite \textit{J. Gou} et al., Physica D 339, 1--17 (2017; Zbl 1376.92020) Full Text: DOI
Hormozi, Sarah; Ward, Michael J. A hybrid asymptotic-numerical method for calculating drag coefficients in 2-D low Reynolds number flows. (English) Zbl 1365.76273 J. Eng. Math. 102, 3-33 (2017). MSC: 76M45 76S05 76Dxx PDFBibTeX XMLCite \textit{S. Hormozi} and \textit{M. J. Ward}, J. Eng. Math. 102, 3--33 (2017; Zbl 1365.76273) Full Text: DOI
Lindsay, Alan E.; Bernoff, Andrew J.; Ward, Michael J. First passage statistics for the capture of a Brownian particle by a structured spherical target with multiple surface traps. (English) Zbl 1372.35021 Multiscale Model. Simul. 15, No. 1, 74-109 (2017). MSC: 35B25 35C20 35J05 35J08 PDFBibTeX XMLCite \textit{A. E. Lindsay} et al., Multiscale Model. Simul. 15, No. 1, 74--109 (2017; Zbl 1372.35021) Full Text: DOI
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng Delayed reaction kinetics and the stability of spikes in the Gierer-Meinhardt model. (English) Zbl 1368.35021 SIAM J. Appl. Math. 77, No. 2, 664-696 (2017). MSC: 35B25 35B35 35K57 35B32 35R10 35Q92 PDFBibTeX XMLCite \textit{N. T. Fadai} et al., SIAM J. Appl. Math. 77, No. 2, 664--696 (2017; Zbl 1368.35021) Full Text: DOI
Moyles, Iain R.; Ward, Michael J. Existence, stability, and dynamics of ring and near-ring solutions to the saturated Gierer-Meinhardt model in the semistrong regime. (English) Zbl 1434.35017 SIAM J. Appl. Dyn. Syst. 16, No. 1, 597-639 (2017). MSC: 35K40 35B25 35B32 35B36 35B40 35K57 35P30 37M20 PDFBibTeX XMLCite \textit{I. R. Moyles} and \textit{M. J. Ward}, SIAM J. Appl. Dyn. Syst. 16, No. 1, 597--639 (2017; Zbl 1434.35017) Full Text: DOI
Tzou, J. C.; Xie, S.; Kolokolnikov, T.; Ward, M. J. The stability and slow dynamics of localized spot patterns for the 3-D Schnakenberg reaction-diffusion model. (English) Zbl 1434.35019 SIAM J. Appl. Dyn. Syst. 16, No. 1, 294-336 (2017). MSC: 35K51 35K57 35K58 35B35 35B36 35B40 35C20 PDFBibTeX XMLCite \textit{J. C. Tzou} et al., SIAM J. Appl. Dyn. Syst. 16, No. 1, 294--336 (2017; Zbl 1434.35019) Full Text: DOI
Tse, W. H.; Ward, M. J. Hotspot formation and dynamics for a continuum model of urban crime. (English) Zbl 1408.91169 Eur. J. Appl. Math. 27, No. 3, 583-624 (2016). MSC: 91D10 35Q91 PDFBibTeX XMLCite \textit{W. H. Tse} and \textit{M. J. Ward}, Eur. J. Appl. Math. 27, No. 3, 583--624 (2016; Zbl 1408.91169) Full Text: DOI
Jamieson-Lane, Alastair; Trinh, Philippe H.; Ward, Michael J. Localized spot patterns on the sphere for reaction-diffusion systems: theory and open problems. (English) Zbl 1357.35189 Bélair, Jacques (ed.) et al., Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7–15, 2015. Cham: Springer (ISBN 978-3-319-30377-2/hbk; 978-3-319-30379-6/ebook). 641-651 (2016). MSC: 35K57 35B36 35R01 PDFBibTeX XMLCite \textit{A. Jamieson-Lane} et al., in: Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7--15, 2015. Cham: Springer. 641--651 (2016; Zbl 1357.35189) Full Text: DOI
Gou, J.; Ward, M. J. An asymptotic analysis of a 2-D model of dynamically active compartments coupled by bulk diffusion. (English) Zbl 1439.92024 J. Nonlinear Sci. 26, No. 4, 979-1029 (2016). MSC: 92B25 35A08 35B20 35B32 35B35 35M33 PDFBibTeX XMLCite \textit{J. Gou} and \textit{M. J. Ward}, J. Nonlinear Sci. 26, No. 4, 979--1029 (2016; Zbl 1439.92024) Full Text: DOI arXiv
Gou, J.; Ward, M. J. Oscillatory dynamics for a coupled membrane-bulk diffusion model with Fitzhugh-Nagumo membrane kinetics. (English) Zbl 1347.35032 SIAM J. Appl. Math. 76, No. 2, 776-804 (2016). MSC: 35B32 35B20 35B35 92B25 35K51 35K58 35B25 PDFBibTeX XMLCite \textit{J. Gou} and \textit{M. J. Ward}, SIAM J. Appl. Math. 76, No. 2, 776--804 (2016; Zbl 1347.35032) Full Text: DOI
Moyles, I.; Tse, W. H.; Ward, M. J. Explicitly solvable nonlocal eigenvalue problems and the stability of localized stripes in reaction-diffusion systems. (English) Zbl 1338.35246 Stud. Appl. Math. 136, No. 1, 89-136 (2016). Reviewer: Denise Huet (Nancy) MSC: 35K57 35B35 35B36 91D10 PDFBibTeX XMLCite \textit{I. Moyles} et al., Stud. Appl. Math. 136, No. 1, 89--136 (2016; Zbl 1338.35246) Full Text: DOI Link
Iron, D.; Rumsey, J.; Ward, M. J.; Wei, J. On accurately estimating stability thresholds for periodic spot patterns of reaction-diffusion systems in \(\mathbb{R}^2\). (English) Zbl 1382.35134 Eur. J. Appl. Math. 26, No. 3, 325-353 (2015). MSC: 35K57 35K40 35B10 35B35 PDFBibTeX XMLCite \textit{D. Iron} et al., Eur. J. Appl. Math. 26, No. 3, 325--353 (2015; Zbl 1382.35134) Full Text: DOI
Tzou, J. C.; Ward, M. J.; Kolokolnikov, T. Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems. (English) Zbl 1364.35151 Physica D 290, 24-43 (2015). MSC: 35K57 35B32 37G10 37M05 PDFBibTeX XMLCite \textit{J. C. Tzou} et al., Physica D 290, 24--43 (2015; Zbl 1364.35151) Full Text: DOI arXiv
Gou, J.; Li, Y. X.; Nagata, W.; Ward, M. J. Synchronized oscillatory dynamics for a 1-D model of membrane kinetics coupled by linear bulk diffusion. (English) Zbl 1331.35038 SIAM J. Appl. Dyn. Syst. 14, No. 4, 2096-2137 (2015). MSC: 35B32 35B20 35B35 92B25 PDFBibTeX XMLCite \textit{J. Gou} et al., SIAM J. Appl. Dyn. Syst. 14, No. 4, 2096--2137 (2015; Zbl 1331.35038) Full Text: DOI
Delgado, M. I.; Ward, M. J.; Coombs, D. Conditional mean first passage times to small traps in a 3-D domain with a sticky boundary: applications to T cell searching behavior in lymph nodes. (English) Zbl 1339.92009 Multiscale Model. Simul. 13, No. 4, 1224-1258 (2015). MSC: 92C17 92C37 35J05 35J08 60J70 PDFBibTeX XMLCite \textit{M. I. Delgado} et al., Multiscale Model. Simul. 13, No. 4, 1224--1258 (2015; Zbl 1339.92009) Full Text: DOI Link
Kurella, Venu; Tzou, Justin; Coombs, Daniel; Ward, Michael Asymptotic analysis of first passage time problems inspired by ecology. (English) Zbl 1319.35275 Bull. Math. Biol. 77, No. 1, 83-125 (2015). MSC: 35Q92 35B25 35J25 92D40 65M75 35C20 PDFBibTeX XMLCite \textit{V. Kurella} et al., Bull. Math. Biol. 77, No. 1, 83--125 (2015; Zbl 1319.35275) Full Text: DOI
Lindsay, A. E.; Ward, M. J.; Kolokolnikov, T. The transition to a point constraint in a mixed biharmonic eigenvalue problem. (English) Zbl 1319.35120 SIAM J. Appl. Math. 75, No. 3, 1193-1224 (2015). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 35P05 35G15 35B25 74K20 PDFBibTeX XMLCite \textit{A. E. Lindsay} et al., SIAM J. Appl. Math. 75, No. 3, 1193--1224 (2015; Zbl 1319.35120) Full Text: DOI Link
Breña-Medina, V. F.; Avitabile, D.; Champneys, A. R.; Ward, M. J. Stripe to spot transition in a plant root hair initiation model. (English) Zbl 06444870 SIAM J. Appl. Math. 75, No. 3, 1090-1119 (2015). MSC: 65-XX 92-XX PDFBibTeX XMLCite \textit{V. F. Breña-Medina} et al., SIAM J. Appl. Math. 75, No. 3, 1090--1119 (2015; Zbl 06444870) Full Text: DOI arXiv
Iron, David; Rumsey, John; Ward, Michael J.; Wei, Juncheng Logarithmic expansions and the stability of periodic patterns of localized spots for reaction-diffusion systems in \(\mathbb R^2\). (English) Zbl 1334.35347 J. Nonlinear Sci. 24, No. 5, 857-912 (2014). Reviewer: Catalin Popa (Iaşi) MSC: 35Q82 35K57 82B20 PDFBibTeX XMLCite \textit{D. Iron} et al., J. Nonlinear Sci. 24, No. 5, 857--912 (2014; Zbl 1334.35347) Full Text: DOI arXiv
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. (English) Zbl 1304.35051 Discrete Contin. Dyn. Syst., Ser. B 19, No. 5, 1373-1410 (2014). MSC: 35B25 35B35 45M05 92D50 92D25 35B32 35Q91 35B36 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Discrete Contin. Dyn. Syst., Ser. B 19, No. 5, 1373--1410 (2014; Zbl 1304.35051) Full Text: DOI arXiv
Rozada, Ignacio; Ruuth, Steven J.; Ward, M. J. The stability of localized spot patterns for the Brusselator on the sphere. (English) Zbl 1302.35033 SIAM J. Appl. Dyn. Syst. 13, No. 1, 564-627 (2014). MSC: 35B25 35K57 35B36 35P05 35B32 35B35 PDFBibTeX XMLCite \textit{I. Rozada} et al., SIAM J. Appl. Dyn. Syst. 13, No. 1, 564--627 (2014; Zbl 1302.35033) Full Text: DOI Link
Breña-Medina, V.; Champneys, A. R.; Grierson, C.; Ward, M. J. Mathematical modeling of plant root hair initiation: dynamics of localized patches. (English) Zbl 1302.35030 SIAM J. Appl. Dyn. Syst. 13, No. 1, 210-248 (2014). MSC: 35B25 35B32 35K57 34B07 35Q92 PDFBibTeX XMLCite \textit{V. Breña-Medina} et al., SIAM J. Appl. Dyn. Syst. 13, No. 1, 210--248 (2014; Zbl 1302.35030) Full Text: DOI Link
Tzou, J. C.; Nec, Y.; Ward, M. J. The stability of localized spikes for the 1-D Brusselator reaction-diffusion model. (English) Zbl 1295.35038 Eur. J. Appl. Math. 24, No. 4, 515-564 (2013). MSC: 35B25 35K57 35K51 35B35 35B32 PDFBibTeX XMLCite \textit{J. C. Tzou} et al., Eur. J. Appl. Math. 24, No. 4, 515--564 (2013; Zbl 1295.35038) Full Text: DOI
Nec, Yana; Ward, Michael J. Dynamics and stability of spike-type solutions to a one dimensional Gierer-Meinhardt model with sub-diffusion. (English) Zbl 1252.35033 Physica D 241, No. 10, 947-963 (2012). MSC: 35B25 35R11 35K51 35K58 35K57 PDFBibTeX XMLCite \textit{Y. Nec} and \textit{M. J. Ward}, Physica D 241, No. 10, 947--963 (2012; Zbl 1252.35033) Full Text: DOI
Cheviakov, A. F.; Ward, M. J. Optimizing the principal eigenvalue of the Laplacian in a sphere with interior traps. (English) Zbl 1219.35155 Math. Comput. Modelling 53, No. 7-8, 1394-1409 (2011). MSC: 35P15 35J05 60J70 PDFBibTeX XMLCite \textit{A. F. Cheviakov} and \textit{M. J. Ward}, Math. Comput. Modelling 53, No. 7--8, 1394--1409 (2011; Zbl 1219.35155) Full Text: DOI
Kropinski, M. C.; Lindsay, A. E.; Ward, M. J. Asymptotic analysis of localized solutions to some linear and nonlinear biharmonic eigenvalue problems. (English) Zbl 1219.35043 Stud. Appl. Math. 126, No. 4, 347-408 (2011). Reviewer: Hans-Christoph Grunau (Magdeburg) MSC: 35C20 35J40 PDFBibTeX XMLCite \textit{M. C. Kropinski} et al., Stud. Appl. Math. 126, No. 4, 347--408 (2011; Zbl 1219.35043) Full Text: DOI
Lindsay, A. E.; Ward, M. J. Asymptotics of some nonlinear eigenvalue problems modelling a MEMS capacitor. II: Multiple solutions and singular asymptotics. (English) Zbl 1220.35108 Eur. J. Appl. Math. 22, No. 2, 83-123 (2011). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 35P30 74K15 35J75 35J25 35B25 PDFBibTeX XMLCite \textit{A. E. Lindsay} and \textit{M. J. Ward}, Eur. J. Appl. Math. 22, No. 2, 83--123 (2011; Zbl 1220.35108) Full Text: DOI
Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J. Similarity: Generalizations, applications and open problems. (English) Zbl 1188.00015 J. Eng. Math. 66, No. 1-3, 1-9 (2010). MSC: 00A71 00A73 70H33 76M55 PDFBibTeX XMLCite \textit{G. Bluman} et al., J. Eng. Math. 66, No. 1--3, 1--9 (2010; Zbl 1188.00015) Full Text: DOI
Kolokolnikov, T.; Ward, M. J.; Wei, J. Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. (English) Zbl 1178.35039 J. Nonlinear Sci. 19, No. 1, 1-56 (2009). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 92E20 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., J. Nonlinear Sci. 19, No. 1, 1--56 (2009; Zbl 1178.35039) Full Text: DOI Link
Chen, Wan; Ward, Michael J. Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model. (English) Zbl 1197.35021 Eur. J. Appl. Math. 20, No. 2, 187-214 (2009). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 80A22 35B32 35Q79 PDFBibTeX XMLCite \textit{W. Chen} and \textit{M. J. Ward}, Eur. J. Appl. Math. 20, No. 2, 187--214 (2009; Zbl 1197.35021) Full Text: DOI
Straube, Ronny; Ward, Michael J.; Falcke, Martin Reaction rate of small diffusing molecules on a cylindrical membrane. (English) Zbl 1206.82150 J. Stat. Phys. 129, No. 2, 377-405 (2007). MSC: 82D60 PDFBibTeX XMLCite \textit{R. Straube} et al., J. Stat. Phys. 129, No. 2, 377--405 (2007; Zbl 1206.82150) Full Text: DOI
Kolokolnikov, T.; Ward, M. J.; Wei, J. Self-replication of mesa patterns in reaction-diffusion systems. (English) Zbl 1136.35002 Physica D 236, No. 2, 104-122 (2007). MSC: 35B25 35K57 35K50 35B32 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Physica D 236, No. 2, 104--122 (2007; Zbl 1136.35002) Full Text: DOI arXiv
Ward, Michael J. Asymptotic methods for reaction-diffusion systems: past and present. (English) Zbl 1334.92004 Bull. Math. Biol. 68, No. 5, 1151-1167 (2006). MSC: 92-03 92C45 92C40 PDFBibTeX XMLCite \textit{M. J. Ward}, Bull. Math. Biol. 68, No. 5, 1151--1167 (2006; Zbl 1334.92004) Full Text: DOI
Kolokolnikov, T.; Ward, M. J.; Wei, J. Zigzag and breakup instabilities of stripes and rings in the two-dimensional Gray-Scott model. (English) Zbl 1145.35388 Stud. Appl. Math. 116, No. 1, 35-95 (2006). MSC: 35K50 35B25 35B40 35K55 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Stud. Appl. Math. 116, No. 1, 35--95 (2006; Zbl 1145.35388) Full Text: DOI
Ou, Chunhua; Ward, Michael J. A metastable flame-front interface and Carrier’s problem. (English) Zbl 1138.80307 J. Comput. Appl. Math. 190, No. 1-2, 354-375 (2006). MSC: 80A25 35B25 35K57 80M25 80M35 PDFBibTeX XMLCite \textit{C. Ou} and \textit{M. J. Ward}, J. Comput. Appl. Math. 190, No. 1--2, 354--375 (2006; Zbl 1138.80307) Full Text: DOI
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: The low feed-rate regime. (English) Zbl 1145.65328 Stud. Appl. Math. 115, No. 1, 21-71 (2005). MSC: 65P40 92E20 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Stud. Appl. Math. 115, No. 1, 21--71 (2005; Zbl 1145.65328) Full Text: DOI
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng Pulse-splitting for some reaction-diffusion systems in one-space dimension. (English) Zbl 1145.35401 Stud. Appl. Math. 114, No. 2, 115-165 (2005). MSC: 35K57 35B25 35K50 92D25 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Stud. Appl. Math. 114, No. 2, 115--165 (2005; Zbl 1145.35401) Full Text: DOI
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng The existence and stability of spike equilibria in the one-dimensional Gray – Scott model on a finite domain. (English) Zbl 1125.35048 Appl. Math. Lett. 18, No. 8, 951-956 (2005). MSC: 35K50 35B25 35B35 35K55 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Appl. Math. Lett. 18, No. 8, 951--956 (2005; Zbl 1125.35048) Full Text: DOI
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. (English) Zbl 1136.35003 Physica D 202, No. 3-4, 258-293 (2005). MSC: 35B25 35B35 35B32 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Physica D 202, No. 3--4, 258--293 (2005; Zbl 1136.35003) Full Text: DOI
Iron, David; Ward, Michael J. The stability and dynamics of hot-spot solutions to two one-dimensional microwave heating models. (English) Zbl 1050.35008 Anal. Appl., Singap. 2, No. 1, 21-70 (2004). Reviewer: Michael I. Gil’ (Beer-Sheva) MSC: 35B25 35K57 35K60 35K55 35B30 PDFBibTeX XMLCite \textit{D. Iron} and \textit{M. J. Ward}, Anal. Appl., Singap. 2, No. 1, 21--70 (2004; Zbl 1050.35008) Full Text: DOI
Iron, David; Ward, Michael J. Spike pinning for the Gierer-Meinhardt model. (English) Zbl 0979.35142 Math. Comput. Simul. 55, No. 4-6, 419-431 (2001). MSC: 35Q80 92D10 PDFBibTeX XMLCite \textit{D. Iron} and \textit{M. J. Ward}, Math. Comput. Simul. 55, No. 4--6, 419--431 (2001; Zbl 0979.35142) Full Text: DOI
Iron, David; Ward, Michael J.; Wei, Juncheng The stability of spike solutions to the one-dimensional Gierer-Meinhardt model. (English) Zbl 0983.35020 Physica D 150, No. 1-2, 25-62 (2001). MSC: 35B35 35B25 35K57 PDFBibTeX XMLCite \textit{D. Iron} et al., Physica D 150, No. 1--2, 25--62 (2001; Zbl 0983.35020) Full Text: DOI
Ward, Michael J. Diffusion and bifurcation problems in singularly perturbed domains. (English) Zbl 1107.35369 Nat. Resour. Model. 13, No. 2, 271-302 (2000). Reviewer: Dietrich Göhde (MR1783276) MSC: 35K57 35B25 PDFBibTeX XMLCite \textit{M. J. Ward}, Nat. Resour. Model. 13, No. 2, 271--302 (2000; Zbl 1107.35369) Full Text: DOI
Ward, M. J. Eliminating indeterminacy for localized solutions to reaction-diffusion equations in multidimensional domains. (English) Zbl 0866.35052 Appl. Math. Lett. 9, No. 6, 47-51 (1996). MSC: 35K57 35B25 PDFBibTeX XMLCite \textit{M. J. Ward}, Appl. Math. Lett. 9, No. 6, 47--51 (1996; Zbl 0866.35052) Full Text: DOI
Ward, Michael J. An asymptotic analysis of localized solutions for some reaction-diffusion model in multidimensional domains. (English) Zbl 0932.35059 Stud. Appl. Math. 97, No. 2, 103-126 (1996). MSC: 35J25 35K57 35B05 35B25 PDFBibTeX XMLCite \textit{M. J. Ward}, Stud. Appl. Math. 97, No. 2, 103--126 (1996; Zbl 0932.35059) Full Text: DOI
Keller, Joseph B.; Ward, Michael J. Asymptotics beyond all orders for a low Reynolds number flow. (English) Zbl 0880.76022 J. Eng. Math. 30, No. 1-2, 253-265 (1996). MSC: 76D99 PDFBibTeX XMLCite \textit{J. B. Keller} and \textit{M. J. Ward}, J. Eng. Math. 30, No. 1--2, 253--265 (1996; Zbl 0880.76022) Full Text: DOI
Reyna, Luis G.; Ward, Michael J. On exponential ill-conditioning and internal layer behavior. (English) Zbl 0828.65114 Numer. Funct. Anal. Optimization 16, No. 3-4, 475-500 (1995). Reviewer: V.A.Kostova (Russe) MSC: 65M30 65M06 35K57 35L67 PDFBibTeX XMLCite \textit{L. G. Reyna} and \textit{M. J. Ward}, Numer. Funct. Anal. Optim. 16, No. 3--4, 475--500 (1995; Zbl 0828.65114) Full Text: DOI
Reyna, Luis G.; Ward, Michael J. On the exponentially slow motion of a viscous shock. (English) Zbl 0824.76042 Commun. Pure Appl. Math. 48, No. 2, 79-120 (1995). Reviewer: A.Jeffrey (Newcastle upon Tyne) MSC: 76L05 35L67 PDFBibTeX XMLCite \textit{L. G. Reyna} and \textit{M. J. Ward}, Commun. Pure Appl. Math. 48, No. 2, 79--120 (1995; Zbl 0824.76042) Full Text: DOI
Lee, June-Yub; Ward, Michael J. On the asymptotic and numerical analyses of exponentially ill-conditioned singularly perturbed boundary value problems. (English) Zbl 0824.65070 Stud. Appl. Math. 94, No. 3, 271-326 (1995). Reviewer: B.Burrows (Stafford) MSC: 65L10 65L08 34B05 34E15 PDFBibTeX XMLCite \textit{J.-Y. Lee} and \textit{M. J. Ward}, Stud. Appl. Math. 94, No. 3, 271--326 (1995; Zbl 0824.65070) Full Text: DOI
Reyna, Luis G.; Ward, Michael J. Resolving weak internal layer interactions for the Ginzburg-Landau equation. (English) Zbl 0816.35061 Eur. J. Appl. Math. 5, No. 4, 495-523 (1994). MSC: 35K60 65M99 65N99 35B25 PDFBibTeX XMLCite \textit{L. G. Reyna} and \textit{M. J. Ward}, Eur. J. Appl. Math. 5, No. 4, 495--523 (1994; Zbl 0816.35061) Full Text: DOI
Ward, Michael J. Metastable patterns, layer collapses, and coarsening for a one- dimensional Ginzburg-Landau equation. (English) Zbl 0794.35119 Stud. Appl. Math. 91, No. 1, 51-93 (1994). MSC: 35Q55 35R35 76V05 PDFBibTeX XMLCite \textit{M. J. Ward}, Stud. Appl. Math. 91, No. 1, 51--93 (1994; Zbl 0794.35119) Full Text: DOI
Ward, M. J.; Reyna, L. G.; Odeh, F. M. Multiple steady state solutions in a multi-junction structure. (English) Zbl 0705.65099 Appl. Math. Lett. 2, No. 4, 395-400 (1989). MSC: 65Z05 35Q60 78A55 65M06 PDFBibTeX XMLCite \textit{M. J. Ward} et al., Appl. Math. Lett. 2, No. 4, 395--400 (1989; Zbl 0705.65099) Full Text: DOI