# zbMATH — the first resource for mathematics

## Cosner, Chris

Compute Distance To:
 Author ID: cosner.chris Published as: Cosner, C.; Cosner, Chris
 Documents Indexed: 123 Publications since 1979, including 3 Books Biographic References: 1 Publication
all top 5

#### Co-Authors

 23 single-authored 62 Cantrell, Robert Stephen 12 Lou, Yuan 9 Ruan, Shigui 5 Beier, John C. 5 Bell, Jonathan 5 Fagan, William F. 5 Schaefer, Philip W. 4 Hutson, Vivian 4 Martínez, Salomé 2 Ali, S. W. 2 Bertiger, William 2 Cantrell, Stephen 2 Chen, Jing 2 DeAngelis, Donald L. 2 Fuller, Douglas O. 2 Gao, Daozhou 2 Lenhart, Suzanne M. 2 Protopopescu, Vladimir A. 2 Rundell, William 2 Schmitt, Klaus 2 Yu, Xiao 2 Zhang, Guoyan 1 Ault, Jerald S. 1 Belgacem, Fethi bin Muhammad 1 Brown, Kenneth J. 1 Casas, Jérôme 1 Chamchod, Farida 1 Cuccu, Fabrizio 1 Dávila, Juan 1 Fleckinger, Jacqueline 1 Guan, Yongtao 1 Hassan, Ali N. 1 Huang, Jicai 1 Impoinvil, D. 1 Kapitanski, Lev 1 Kshatriya, Mrigesh 1 Lam, King-Yeung 1 Lazer, Alan C. 1 Lewis, Mark Alun 1 Lutscher, Frithjof 1 Maciel, Gabriel 1 Magal, Christelle 1 Manasevich, Raul F. 1 Nevai, Andrew L. 1 Olson, Donald B. 1 Padrón, Víctor 1 Porru, Giovanni 1 Potts, Matthew D. 1 Protter, Murray H. 1 Schindler, Frank 1 Schreiber, Sebastian J. 1 Shen, Wenxian 1 Torres, Nicolás 1 Troyo, A. 1 Vandendriessche, Peter 1 Winkler, Michael 1 Xie, Chao 1 Zhang, Juping 1 Zhu, Huaiping
all top 5

#### Serials

 11 Journal of Mathematical Biology 8 Mathematical Biosciences 8 Journal of Differential Equations 7 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Journal of Mathematical Analysis and Applications 6 Rocky Mountain Journal of Mathematics 5 Bulletin of Mathematical Biology 5 Theoretical Population Biology 5 SIAM Journal on Mathematical Analysis 4 SIAM Journal on Applied Mathematics 4 Discrete and Continuous Dynamical Systems. Series B 3 Houston Journal of Mathematics 3 Mathematical Biosciences and Engineering 3 Journal of Biological Dynamics 3 Nonlinear Analysis. Theory, Methods & Applications 2 Applicable Analysis 2 Indiana University Mathematics Journal 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Communications in Partial Differential Equations 2 Electronic Journal of Differential Equations (EJDE) 2 Journal of Theoretical Biology 1 IMA Journal of Applied Mathematics 1 Quarterly of Applied Mathematics 1 Results in Mathematics 1 Differential and Integral Equations 1 Dynamic Systems and Applications 1 SIAM Review 1 Journal of Dynamics and Differential Equations 1 The Canadian Applied Mathematics Quarterly 1 Discrete and Continuous Dynamical Systems 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Natural Resource Modeling 1 Advanced Nonlinear Studies 1 Mathematical Medicine and Biology 1 Rendiconti di Matematica, VI. Serie 1 Science China. Mathematics 1 Chapman & Hall/CRC Mathematical and Computational Biology Series
all top 5

#### Fields

 99 Partial differential equations (35-XX) 83 Biology and other natural sciences (92-XX) 21 Ordinary differential equations (34-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Operator theory (47-XX) 4 Probability theory and stochastic processes (60-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 1 Difference and functional equations (39-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH

112 Publications have been cited 2,561 times in 1,580 Documents Cited by Year
Spatial ecology via reaction-diffusion equations. Zbl 1059.92051
Cantrell, Robert Stephen; Cosner, Chris
2003
On the dynamics of predator-prey models with the Beddington-DeAngelis functional response. Zbl 0991.34046
Cantrell, Robert Stephen; Cosner, Chris
2001
Effects of spatial grouping on the functional response of predators. Zbl 0928.92031
Cosner, Chris; DeAngelis, Donald L.; Ault, Jerald S.; Olson, Donald B.
1999
Stable coexistence states in the Volterra-Lotka competition model with diffusion. Zbl 0562.92012
Cosner, Chris; Lazer, A. C.
1984
Diffusive logistic equations with indefinite weights: Population models in disrupted environments. Zbl 0711.92020
Cantrell, Robert Stephen; Cosner, Chris
1989
Diffusive logistic equations with indefinite weights: Population models in disrupted environments. II. Zbl 0726.92024
Cantrell, Robert Stephen; Cosner, Chris
1991
The effects of spatial heterogeneity in population dynamics. Zbl 0722.92018
Cantrell, R. S.; Cosner, C.
1991
Permanence in ecological systems with spatial heterogeneity. Zbl 0796.92026
Cantrell, Robert Stephen; Cosner, Chris; Hutson, Vivian
1993
Threshold behavior and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons. Zbl 0536.34050
Bell, Jonathan; Cosner, Chris
1984
Spatial ecology via reaction-difusion equations. Zbl 1087.92058
Cantrell, Robert Stephen; Cosner, Chris
2003
Advection-mediated coexistence of competing species. Zbl 1139.35048
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2007
The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environments. Zbl 0854.35053
Belgacem, Fethi; Cosner, Chris
1995
Movement toward better environments and the evolution of rapid diffusion. Zbl 1105.92036
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2006
Evolution of dispersal and the ideal free distribution. Zbl 1188.35102
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2010
The effects of human movement on the persistence of vector-borne diseases. Zbl 1402.92386
Cosner, C.; Beier, J. C.; Cantrell, R. S.; Impoinvil, D.; Kapitanski, L.; Potts, M. D.; Troyo, A.; Ruan, S.
2009
Does movement toward better environments always benefit a population? Zbl 1015.92040
Cosner, Chris; Lou, Yuan
2003
On the effects of spatial heterogeneity on the persistence of interacting species. Zbl 0948.92021
Cantrell, Robert Stephen; Cosner, Chris
1998
Ecological models, permanence and spatial heterogeneity. Zbl 0851.92019
Cantrell, Robert Stephen; Cosner, Chris; Hutson, Vivian
1996
The ideal free distribution as an evolutionarily stable strategy. Zbl 1122.92062
Cantrell, Robert Stephen; Cosner, Chris; Deangelis, Donald L.; Padron, Victor
2007
Approximating the ideal free distribution via reaction-diffusion-advection equations. Zbl 1168.35002
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2008
Deriving reaction-diffusion models in ecology from interacting particle systems. Zbl 1058.92041
Cantrell, R. S.; Cosner, C.
2004
Principal eigenvalues for problems with indefinite weight function on $$R^ N$$. Zbl 0726.35089
Brown, K. J.; Cosner, C.; Fleckinger, J.
1990
Reaction-diffusion-advection models for the effects and evolution of dispersal. Zbl 1277.35002
Cosner, Chris
2014
Evolutionary stability of ideal free dispersal strategies in patchy environments. Zbl 1267.34097
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2012
On the steady-state problem for the Volterra-Lotka competition model with diffusion. Zbl 0644.92016
Cantrell, Robert Stephen; Cosner, Chris
1987
Intraspecific interference and consumer-resource dynamics. Zbl 1100.92061
Cantrell, Robert Stephen; Cosner, Chris; Ruan, Shigui
2004
Diffusion models for population dynamics incorporating individual behavior at boundaries: Applications to refuge design. Zbl 0958.92028
Cantrell, R. S.; Cosner, C.
1999
A dynamic model for the ideal-free distribution as a partial differential equation. Zbl 1072.92049
Cosner, Chris
2005
Should a park be an island? Zbl 0811.92022
Cantrell, Robert Stephen; Cosner, Chris
1993
Variability, vagueness and comparison methods for ecological models. Zbl 0878.92029
Cosner, Chris
1996
Global bifurcation of solutions for crime modeling equations. Zbl 1248.35212
Cantrell, Robert Stephen; Cosner, Chris; Manásevich, Raúl
2012
Practical persistence in ecological models via comparison methods. Zbl 0845.92023
Cantrell, Robert Stephen; Cosner, Chris
1996
Density dependent behavior at habitat boundaries and the Allee effect. Zbl 1298.92111
Cantrell, Robert Stephen; Cosner, Chris
2007
Permanence in some diffusive Lotka-Volterra models for three interacting species. Zbl 0795.92030
Cantrell, Robert Stephen; Cosner, Chris; Hutson, Vivian
1993
Competitive reversals inside ecological reserves: The role of external habitat degradation. Zbl 0924.92020
Cantrell, Robert Stephen; Cosner, Chris; Fagan, William F.
1998
Positive solutions for superlinear elliptic systems without variational structure. Zbl 0524.35049
Cosner, Chris
1984
Random dispersal versus fitness-dependent dispersal. Zbl 1263.35203
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan; Xie, Chao
2013
Evolution of dispersal in heterogeneous landscapes. Zbl 1178.92043
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2010
Conditional persistence in logistic models via nonlinear diffusion. Zbl 1042.35023
Cantrell, Robert Stephen; Cosner, Chris
2002
Effects of domain size on the persistence of populations in a diffusive food-chain model with Beddington-DeAngelis functional response. Zbl 1005.92035
Cantrell, Robert Stephen; Cosner, Chris
2001
On the uniqueness of the positive steady state for Lotka-Volterra models with diffusion. Zbl 0799.35115
Ali, S. W.; Cosner, C.
1992
Bifurcation from higher eigenvalues in nonlinear elliptic equations: Continua that meet infinity. Zbl 0695.35011
Cosner, Chris
1988
Global bifurcation of solutions to diffusive logistic equations on bounded domains subject to nonlinear boundary conditions. Zbl 1163.35002
Cantrell, Robert Stephen; Cosner, Chris; Martínez, Salome
2009
On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains. Zbl 1154.35381
Cantrell, Robert Stephen; Cosner, Chris
2006
Modeling and control of local outbreaks of West Nile virus in the United States. Zbl 1351.37272
Chen, Jing; Huang, Jicai; Beier, John C.; Cantrell, Robert Stephen; Cosner, Chris; Fuller, Douglas O.; Zhang, Guoyan; Ruan, Shigui
2016
On the uniqueness and stability of positive solutions in the Lotka- Volterra competition model with diffusion. Zbl 0721.92025
Cantrell, Robert Stephen; Cosner, Chris
1989
Well-posedness and qualitative properties of a dynamical model for the ideal free distribution. Zbl 1317.35116
Cosner, Chris; Winkler, Michael
2014
Modeling the spatial spread of rift valley fever in Egypt. Zbl 1273.92033
Gao, Daozhou; Cosner, Chris; Cantrell, Robert Stephen; Beier, John C.; Ruan, Shigui
2013
Multiple reversals of competitive dominance in ecological reserves via external habitat degradation. Zbl 1065.35140
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2004
Brucellosis, botflies, and brainworms: The impact of edge habitats on pathogen transmission and species extinction. Zbl 1005.92033
Cantrell, Robert Stephen; Cosner, Chris; Fagan, William F.
2001
Models for predator-prey systems at multiple scales. Zbl 0856.92019
Cantrell, R. S.; Cosner, C.
1996
On the positone problem for elliptic systems. Zbl 0596.35034
Cantrell, Robert Stephen; Cosner, Chris
1985
Spatial ecology. Zbl 1173.91013
Cantrell, Stephen (ed.); Cosner, Chris (ed.); Ruan, Shigui (ed.)
2010
Insular biogeographic theory and diffusion models in population dynamics. Zbl 0798.92029
Cantrell, R. S.; Cosner, C.
1994
Pointwise a priori bounds for strongly coupled semi-linear systems of parabolic partial differential equations. Zbl 0467.35014
Cosner, Chris
1981
Comparison principles for systems that embed in cooperative systems, with applications to diffusive Lotka-Volterra models. Zbl 0885.35015
Cosner, Chris
1997
Parabolic systems with nonlinear competitive interactions. Zbl 0716.35033
Cosner, C.; Lenhart, S.; Protopopescu, V.
1990
Models for the effects of host movement in vector-borne disease systems. Zbl 1364.92041
Cosner, Chris
2015
A modeling approach to investigate epizootic outbreaks and enzootic maintenance of rift valley fever virus. Zbl 1300.92093
Chamchod, Farida; Cantrell, Robert Stephen; Cosner, Chris; Hassan, Ali N.; Beier, John C.; Ruan, Shigui
2014
Beyond diffusion: conditional dispersal in ecological models. Zbl 1402.92339
Cosner, Chris
2012
The implications of model formulation when transitioning from spatial to landscape ecology. Zbl 1260.92110
Cantrell, Robert Stephen; Cosner, Chris; Fagan, William F.
2012
Reaction-diffusion equations and ecological modeling. Zbl 1300.92106
Cosner, C.
2008
A continuum formulation of the ideal free distribution and its implications for population dynamics. Zbl 1038.92031
Kshatriya, Mrigesh; Cosner, Chris
2002
Models for the effects of individual size and spatial scale on competition between species in heterogeneous environments. Zbl 0821.92023
Ali, S. W.; Cosner, C.
1995
Sign-definite solutions in some linear elliptic systems. Zbl 0678.35024
Cosner, Chris; Schaefer, Philip W.
1989
On the geometry of level sets of positive solutions of semilinear elliptic equations. Zbl 0706.35022
Cosner, Chris; Schmitt, Klaus
1988
On the generalized spectrum for second-order elliptic systems. Zbl 0652.35084
Cantrell, Robert Stephen; Cosner, Chris
1987
On the development of functionals which satisfy a maximum principle. Zbl 0607.34049
Cosner, Chris; Schaefer, Philip W.
1987
Estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems. Zbl 0545.35070
Cosner, Chris
1984
Threshold conditions for a diffusive model of a myelinated axon. Zbl 0542.92009
Bell, J.; Cosner, C.
1983
Habitat fragmentation promotes malaria persistence. Zbl 1431.92133
Gao, Daozhou; van den Driessche, P.; Cosner, Chris
2019
Resident-invader dynamics in infinite dimensional systems. Zbl 1388.35119
Cantrell, Robert Stephen; Cosner, Chris; Lam, King-Yeung
2017
Evolution of natal dispersal in spatially heterogenous environments. Zbl 1353.92075
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan; Schreiber, Sebastian J.
2017
Spatial population dynamics in a producer-scrounger model. Zbl 1364.92032
Cosner, Chris; Nevai, Andrew L.
2015
Optimization of the first eigenvalue of equations with indefinite weights. Zbl 1410.49055
Cosner, Chris; Cuccu, Fabrizio; Porru, Giovanni
2013
Steady state solutions of a logistic equation with nonlinear boundary conditions. Zbl 1220.35057
Cantrell, Robert S.; Cosner, Chris; Martínez, Salomé
2011
Control of invasive hosts by generalist parasitoids. Zbl 1146.92033
Magal, Christelle; Cosner, Chris; Ruan, Shigui; Casas, Jérôme
2008
On the definition of ellipticity for systems of partial differential equations. Zbl 0746.35012
Cosner, Chris
1991
A maximum principle for weakly coupled systems of second order partial differential equations with nonnegative characteristic form. Zbl 0438.35017
Cosner, Chris
1981
Stability properties of a model of parallel nerve fibers. Zbl 0431.92010
Bell, Jonathan; Cosner, Chris
1981
Asymptotic behavior of solutions of second order parabolic partial differential equations with unbounded coefficients. Zbl 0403.35044
Cosner, Chris
1980
Habitat edges and predator-prey interactions: Effects on critical patch size. Zbl 1005.92034
Cantrell, Robert Stephen; Cosner, Chris; Fagan, William F.
2002
A comparison of foraging strategies in a patchy environment. Zbl 0948.92024
Cantrell, Robert Stephen; Cosner, Chris
1999
Skew Brownian motion: A model for diffusion with interfaces? Zbl 0927.60078
Cantrell, R. S.; Cosner, C.
1998
Persistence (permanence), compressivity, and practical persistence in some reaction-diffusion models from ecology. Zbl 0828.35059
Cosner, Chris
1994
Existence of global solutions to a model of a myelinated nerve axon. Zbl 0642.35075
Cosner, Chris
1987
A comparison principle for a class of fourth-order elliptic operators. Zbl 0634.35006
Cosner, Chris; Schaefer, Philip W.
1987
Threshold conditions for two diffusion models suggested by nerve impulse conduction. Zbl 0609.92014
Bell, Jonathan; Cosner, Chris
1986
A priori bounds for positive solutions of a semilinear elliptic equation. Zbl 0577.35041
Cosner, Chris; Schmitt, Klaus
1985
Pointwise bounds for strongly coupled time dependent systems of reaction- diffusion equations. Zbl 0548.35070
Cosner, Chris
1984
Systems of second order equations with nonnegative characteristic form. Zbl 0427.35033
Bertiger, William; Cosner, Chris
1979
Evolutionarily stable movement strategies in reaction-diffusion models with edge behavior. Zbl 1433.92066
Maciel, Gabriel; Cosner, Chris; Cantrell, Robert Stephen; Lutscher, Frithjof
2020
Two-patch model for the spread of West Nile virus. Zbl 1390.92153
Zhang, Juping; Cosner, Chris; Zhu, Huaiping
2018
Upper and lower solutions for a homogeneous Dirichlet problem with nonlinear diffusion and the principle of linearized stability. Zbl 1002.35017
Cantrell, Robert Stephen; Cosner, Chris
2000
Bounds and trajectories in diffusive predator-prey models. Zbl 0928.92030
Cantrell, R. S.; Cosner, C.
1997
Spatially explicit models for the population dynamics of a species colonizing an island. Zbl 0860.92028
Cantrell, R. S.; Cosner, C.; Hutson, V.
1996
Eigenvalue problems with indefinite weights and reaction-diffusion models in population dynamics. Zbl 0733.35054
Cosner, Chris
1990
Transport equations with second-order differential collision operators. Zbl 0654.35054
Cosner, Chris; Lenhart, Suzanne M.; Protopopescu, Vladimir
1988
Bounds for the spectrum and the norm of solutions of nonlinear elliptic equations and systems. Zbl 0513.35069
Cosner, C.; Protter, M. H.
1985
Extension of solutions to second order partial differential equations by the method of quasireversibility. Zbl 0564.35006
Cosner, Chris; Rundell, William
1984
Evolutionarily stable movement strategies in reaction-diffusion models with edge behavior. Zbl 1433.92066
Maciel, Gabriel; Cosner, Chris; Cantrell, Robert Stephen; Lutscher, Frithjof
2020
Populations with individual variation in dispersal in heterogeneous environments: dynamics and competition with simply diffusing populations. Zbl 07177489
Cantrell, Robert Stephen; Cosner, Chris; Yu, Xiao
2020
Habitat fragmentation promotes malaria persistence. Zbl 1431.92133
Gao, Daozhou; van den Driessche, P.; Cosner, Chris
2019
Two-patch model for the spread of West Nile virus. Zbl 1390.92153
Zhang, Juping; Cosner, Chris; Zhu, Huaiping
2018
Evolutionary stability of ideal free dispersal under spatial heterogeneity and time periodicity. Zbl 1409.92261
Cantrell, Robert Stephen; Cosner, Chris
2018
On a competitive system with ideal free dispersal. Zbl 06901109
Cantrell, Robert Stephen; Cosner, Chris; Martínez, Salomé; Torres, Nicolás
2018
Resident-invader dynamics in infinite dimensional systems. Zbl 1388.35119
Cantrell, Robert Stephen; Cosner, Chris; Lam, King-Yeung
2017
Evolution of natal dispersal in spatially heterogenous environments. Zbl 1353.92075
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan; Schreiber, Sebastian J.
2017
Modeling and control of local outbreaks of West Nile virus in the United States. Zbl 1351.37272
Chen, Jing; Huang, Jicai; Beier, John C.; Cantrell, Robert Stephen; Cosner, Chris; Fuller, Douglas O.; Zhang, Guoyan; Ruan, Shigui
2016
Models for the effects of host movement in vector-borne disease systems. Zbl 1364.92041
Cosner, Chris
2015
Spatial population dynamics in a producer-scrounger model. Zbl 1364.92032
Cosner, Chris; Nevai, Andrew L.
2015
Reaction-diffusion-advection models for the effects and evolution of dispersal. Zbl 1277.35002
Cosner, Chris
2014
Well-posedness and qualitative properties of a dynamical model for the ideal free distribution. Zbl 1317.35116
Cosner, Chris; Winkler, Michael
2014
A modeling approach to investigate epizootic outbreaks and enzootic maintenance of rift valley fever virus. Zbl 1300.92093
Chamchod, Farida; Cantrell, Robert Stephen; Cosner, Chris; Hassan, Ali N.; Beier, John C.; Ruan, Shigui
2014
Random dispersal versus fitness-dependent dispersal. Zbl 1263.35203
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan; Xie, Chao
2013
Modeling the spatial spread of rift valley fever in Egypt. Zbl 1273.92033
Gao, Daozhou; Cosner, Chris; Cantrell, Robert Stephen; Beier, John C.; Ruan, Shigui
2013
Optimization of the first eigenvalue of equations with indefinite weights. Zbl 1410.49055
Cosner, Chris; Cuccu, Fabrizio; Porru, Giovanni
2013
Evolutionary stability of ideal free dispersal strategies in patchy environments. Zbl 1267.34097
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2012
Global bifurcation of solutions for crime modeling equations. Zbl 1248.35212
Cantrell, Robert Stephen; Cosner, Chris; Manásevich, Raúl
2012
Beyond diffusion: conditional dispersal in ecological models. Zbl 1402.92339
Cosner, Chris
2012
The implications of model formulation when transitioning from spatial to landscape ecology. Zbl 1260.92110
Cantrell, Robert Stephen; Cosner, Chris; Fagan, William F.
2012
Steady state solutions of a logistic equation with nonlinear boundary conditions. Zbl 1220.35057
Cantrell, Robert S.; Cosner, Chris; Martínez, Salomé
2011
Evolution of dispersal and the ideal free distribution. Zbl 1188.35102
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2010
Evolution of dispersal in heterogeneous landscapes. Zbl 1178.92043
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2010
Spatial ecology. Zbl 1173.91013
Cantrell, Stephen (ed.); Cosner, Chris (ed.); Ruan, Shigui (ed.)
2010
The effects of human movement on the persistence of vector-borne diseases. Zbl 1402.92386
Cosner, C.; Beier, J. C.; Cantrell, R. S.; Impoinvil, D.; Kapitanski, L.; Potts, M. D.; Troyo, A.; Ruan, S.
2009
Global bifurcation of solutions to diffusive logistic equations on bounded domains subject to nonlinear boundary conditions. Zbl 1163.35002
Cantrell, Robert Stephen; Cosner, Chris; Martínez, Salome
2009
Approximating the ideal free distribution via reaction-diffusion-advection equations. Zbl 1168.35002
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2008
Reaction-diffusion equations and ecological modeling. Zbl 1300.92106
Cosner, C.
2008
Control of invasive hosts by generalist parasitoids. Zbl 1146.92033
Magal, Christelle; Cosner, Chris; Ruan, Shigui; Casas, Jérôme
2008
Advection-mediated coexistence of competing species. Zbl 1139.35048
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2007
The ideal free distribution as an evolutionarily stable strategy. Zbl 1122.92062
Cantrell, Robert Stephen; Cosner, Chris; Deangelis, Donald L.; Padron, Victor
2007
Density dependent behavior at habitat boundaries and the Allee effect. Zbl 1298.92111
Cantrell, Robert Stephen; Cosner, Chris
2007
Movement toward better environments and the evolution of rapid diffusion. Zbl 1105.92036
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2006
On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains. Zbl 1154.35381
Cantrell, Robert Stephen; Cosner, Chris
2006
A dynamic model for the ideal-free distribution as a partial differential equation. Zbl 1072.92049
Cosner, Chris
2005
Deriving reaction-diffusion models in ecology from interacting particle systems. Zbl 1058.92041
Cantrell, R. S.; Cosner, C.
2004
Intraspecific interference and consumer-resource dynamics. Zbl 1100.92061
Cantrell, Robert Stephen; Cosner, Chris; Ruan, Shigui
2004
Multiple reversals of competitive dominance in ecological reserves via external habitat degradation. Zbl 1065.35140
Cantrell, Robert Stephen; Cosner, Chris; Lou, Yuan
2004
Spatial ecology via reaction-diffusion equations. Zbl 1059.92051
Cantrell, Robert Stephen; Cosner, Chris
2003
Spatial ecology via reaction-difusion equations. Zbl 1087.92058
Cantrell, Robert Stephen; Cosner, Chris
2003
Does movement toward better environments always benefit a population? Zbl 1015.92040
Cosner, Chris; Lou, Yuan
2003
Conditional persistence in logistic models via nonlinear diffusion. Zbl 1042.35023
Cantrell, Robert Stephen; Cosner, Chris
2002
A continuum formulation of the ideal free distribution and its implications for population dynamics. Zbl 1038.92031
Kshatriya, Mrigesh; Cosner, Chris
2002
Habitat edges and predator-prey interactions: Effects on critical patch size. Zbl 1005.92034
Cantrell, Robert Stephen; Cosner, Chris; Fagan, William F.
2002
On the dynamics of predator-prey models with the Beddington-DeAngelis functional response. Zbl 0991.34046
Cantrell, Robert Stephen; Cosner, Chris
2001
Effects of domain size on the persistence of populations in a diffusive food-chain model with Beddington-DeAngelis functional response. Zbl 1005.92035
Cantrell, Robert Stephen; Cosner, Chris
2001
Brucellosis, botflies, and brainworms: The impact of edge habitats on pathogen transmission and species extinction. Zbl 1005.92033
Cantrell, Robert Stephen; Cosner, Chris; Fagan, William F.
2001
Upper and lower solutions for a homogeneous Dirichlet problem with nonlinear diffusion and the principle of linearized stability. Zbl 1002.35017
Cantrell, Robert Stephen; Cosner, Chris
2000
Contributions of Alan C. Lazer to mathematical population dynamics. Zbl 1056.92045
Cosner, Chris
2000
Effects of spatial grouping on the functional response of predators. Zbl 0928.92031
Cosner, Chris; DeAngelis, Donald L.; Ault, Jerald S.; Olson, Donald B.
1999
Diffusion models for population dynamics incorporating individual behavior at boundaries: Applications to refuge design. Zbl 0958.92028
Cantrell, R. S.; Cosner, C.
1999
A comparison of foraging strategies in a patchy environment. Zbl 0948.92024
Cantrell, Robert Stephen; Cosner, Chris
1999
On the effects of spatial heterogeneity on the persistence of interacting species. Zbl 0948.92021
Cantrell, Robert Stephen; Cosner, Chris
1998
Competitive reversals inside ecological reserves: The role of external habitat degradation. Zbl 0924.92020
Cantrell, Robert Stephen; Cosner, Chris; Fagan, William F.
1998
Skew Brownian motion: A model for diffusion with interfaces? Zbl 0927.60078
Cantrell, R. S.; Cosner, C.
1998
Comparison principles for systems that embed in cooperative systems, with applications to diffusive Lotka-Volterra models. Zbl 0885.35015
Cosner, Chris
1997
Bounds and trajectories in diffusive predator-prey models. Zbl 0928.92030
Cantrell, R. S.; Cosner, C.
1997
Ecological models, permanence and spatial heterogeneity. Zbl 0851.92019
Cantrell, Robert Stephen; Cosner, Chris; Hutson, Vivian
1996
Variability, vagueness and comparison methods for ecological models. Zbl 0878.92029
Cosner, Chris
1996
Practical persistence in ecological models via comparison methods. Zbl 0845.92023
Cantrell, Robert Stephen; Cosner, Chris
1996
Models for predator-prey systems at multiple scales. Zbl 0856.92019
Cantrell, R. S.; Cosner, C.
1996
Spatially explicit models for the population dynamics of a species colonizing an island. Zbl 0860.92028
Cantrell, R. S.; Cosner, C.; Hutson, V.
1996
The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environments. Zbl 0854.35053
Belgacem, Fethi; Cosner, Chris
1995
Models for the effects of individual size and spatial scale on competition between species in heterogeneous environments. Zbl 0821.92023
Ali, S. W.; Cosner, C.
1995
Insular biogeographic theory and diffusion models in population dynamics. Zbl 0798.92029
Cantrell, R. S.; Cosner, C.
1994
Persistence (permanence), compressivity, and practical persistence in some reaction-diffusion models from ecology. Zbl 0828.35059
Cosner, Chris
1994
Permanence in ecological systems with spatial heterogeneity. Zbl 0796.92026
Cantrell, Robert Stephen; Cosner, Chris; Hutson, Vivian
1993
Should a park be an island? Zbl 0811.92022
Cantrell, Robert Stephen; Cosner, Chris
1993
Permanence in some diffusive Lotka-Volterra models for three interacting species. Zbl 0795.92030
Cantrell, Robert Stephen; Cosner, Chris; Hutson, Vivian
1993
On the uniqueness of the positive steady state for Lotka-Volterra models with diffusion. Zbl 0799.35115
Ali, S. W.; Cosner, C.
1992
Diffusive logistic equations with indefinite weights: Population models in disrupted environments. II. Zbl 0726.92024
Cantrell, Robert Stephen; Cosner, Chris
1991
The effects of spatial heterogeneity in population dynamics. Zbl 0722.92018
Cantrell, R. S.; Cosner, C.
1991
On the definition of ellipticity for systems of partial differential equations. Zbl 0746.35012
Cosner, Chris
1991
Principal eigenvalues for problems with indefinite weight function on $$R^ N$$. Zbl 0726.35089
Brown, K. J.; Cosner, C.; Fleckinger, J.
1990
Parabolic systems with nonlinear competitive interactions. Zbl 0716.35033
Cosner, C.; Lenhart, S.; Protopopescu, V.
1990
Eigenvalue problems with indefinite weights and reaction-diffusion models in population dynamics. Zbl 0733.35054
Cosner, Chris
1990
Diffusive logistic equations with indefinite weights: Population models in disrupted environments. Zbl 0711.92020
Cantrell, Robert Stephen; Cosner, Chris
1989
On the uniqueness and stability of positive solutions in the Lotka- Volterra competition model with diffusion. Zbl 0721.92025
Cantrell, Robert Stephen; Cosner, Chris
1989
Sign-definite solutions in some linear elliptic systems. Zbl 0678.35024
Cosner, Chris; Schaefer, Philip W.
1989
Sign-definite solutions in elliptic systems with constant coefficients. Zbl 0723.35016
Schaefer, Philip; Cosner, Chris
1989
On eigenfunctions with sign definite components in weakly coupled linear elliptic systems. Zbl 0686.35038
Cantrell, Robert Stephen; Cosner, Chris
1989
On the complex spectra of second order elliptic systems. Zbl 0681.35065
Cosner, Chris
1989
Bifurcation from higher eigenvalues in nonlinear elliptic equations: Continua that meet infinity. Zbl 0695.35011
Cosner, Chris
1988
On the geometry of level sets of positive solutions of semilinear elliptic equations. Zbl 0706.35022
Cosner, Chris; Schmitt, Klaus
1988
Transport equations with second-order differential collision operators. Zbl 0654.35054
Cosner, Chris; Lenhart, Suzanne M.; Protopopescu, Vladimir
1988
On the convex case in the positone problem for elliptic systems. Zbl 0671.35029
Cantrell, Robert Stephen; Cosner, Chris
1988
On the steady-state problem for the Volterra-Lotka competition model with diffusion. Zbl 0644.92016
Cantrell, Robert Stephen; Cosner, Chris
1987
On the generalized spectrum for second-order elliptic systems. Zbl 0652.35084
Cantrell, Robert Stephen; Cosner, Chris
1987
On the development of functionals which satisfy a maximum principle. Zbl 0607.34049
Cosner, Chris; Schaefer, Philip W.
1987
Existence of global solutions to a model of a myelinated nerve axon. Zbl 0642.35075
Cosner, Chris
1987
A comparison principle for a class of fourth-order elliptic operators. Zbl 0634.35006
Cosner, Chris; Schaefer, Philip W.
1987
Threshold conditions for two diffusion models suggested by nerve impulse conduction. Zbl 0609.92014
Bell, Jonathan; Cosner, Chris
1986
On the positone problem for elliptic systems. Zbl 0596.35034
Cantrell, Robert Stephen; Cosner, Chris
1985
A priori bounds for positive solutions of a semilinear elliptic equation. Zbl 0577.35041
Cosner, Chris; Schmitt, Klaus
1985
Bounds for the spectrum and the norm of solutions of nonlinear elliptic equations and systems. Zbl 0513.35069
Cosner, C.; Protter, M. H.
1985
Stable coexistence states in the Volterra-Lotka competition model with diffusion. Zbl 0562.92012
Cosner, Chris; Lazer, A. C.
1984
Threshold behavior and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons. Zbl 0536.34050
Bell, Jonathan; Cosner, Chris
1984
Positive solutions for superlinear elliptic systems without variational structure. Zbl 0524.35049
Cosner, Chris
1984
Estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems. Zbl 0545.35070
Cosner, Chris
1984
...and 12 more Documents
all top 5

#### Cited by 1,978 Authors

 57 Cosner, Chris 49 Lou, Yuan 41 Cantrell, Robert Stephen 31 Shi, Junping 25 Li, Wan-Tong 23 Wang, Weiming 22 Lin, Zhigui 20 Ruan, Shigui 20 Zhao, Xiao-Qiang 19 Lutscher, Frithjof 19 Suárez, Antonio 18 Lam, King-Yeung 17 López-Gómez, Julián 17 Wang, Yuanshi 16 Cai, Yongli 16 Du, Yihong 13 Ahn, Inkyung 13 Wang, Mingxin 13 Zhou, Jun 13 Zou, Xingfu 12 Peng, Rui 12 Shen, Wenxian 12 Shivaji, Ratnasingham 12 Wu, Jianhua 11 DeAngelis, Donald L. 11 Lewis, Mark Alun 11 Pao, Chia-Ven 10 Delgado, Manuel 10 Kumar Upadhyay, Ranjit 10 Ni, Wei-Ming 10 Umezu, Kenichiro 10 Zhang, Jiafang 10 Zhou, Peng 9 Banerjee, Malay 9 Chen, Youpeng 9 Gao, Daozhou 9 Guo, Shangjiang 9 He, Xiaoqing 9 Ko, Wonlyul 9 Morales-Rodrigo, Cristian 9 Roques, Lionel J. 9 Wu, Hong 8 Hamel, François 8 Lenhart, Suzanne M. 8 Liu, Shengqiang 8 Wang, Jinfeng 8 Wang, Yuxia 7 Chen, Lansun 7 Feng, Wei 7 Jana, Debaldev 7 Lejay, Antoine 7 Rao, Feng 7 Schreiber, Sebastian J. 7 Wang, Bixiang 7 Wang, Qi 7 Winkler, Michael 7 Wu, YiXiang 7 Xiao, Dongmei 7 Xie, Chunhong 7 Zhu, Min 6 Baek, Hunki 6 Bai, Xueli 6 Capone, Florinda 6 Cui, Renhao 6 Dancer, Edward Norman 6 Fan, Meng 6 Goddard, Jerome II 6 Hutson, Vivian 6 Kang, Yun 6 Ma, Li 6 Nie, Hua 6 Rionero, Salvatore 6 Ryu, Kimun 6 Song, Yongli 6 Tang, De 6 Teng, Zhi-dong 6 Tripathi, Jai Prakash 6 Verzini, Gianmaria 6 Wang, Wendi 6 Wang, Yuanming 6 Wei, Junjie 6 Yan, Xiangping 5 Abdallah, Ahmed Y. 5 Cao, Jia-Feng 5 Caraballo Garrido, Tomás 5 Chen, Shanshan 5 Chen, Yuming 5 Choi, Wonhyung 5 Cintra, Willian 5 Dai, Binxiang 5 Dai, Guowei 5 De Luca, Roberta 5 Fu, Shengmao 5 Gao, Wenjie 5 Haque, Mainul 5 Kamrujjaman, Md. 5 Kawasaki, Kohkichi 5 Lee, Eunkyoung 5 Lin, Guo 5 Lu, Xin ...and 1,878 more Authors
all top 5

#### Cited in 216 Serials

 116 Journal of Differential Equations 113 Journal of Mathematical Analysis and Applications 78 Journal of Mathematical Biology 78 Nonlinear Analysis. Real World Applications 63 Discrete and Continuous Dynamical Systems. Series B 62 Applied Mathematics and Computation 53 Bulletin of Mathematical Biology 48 Mathematical Biosciences 42 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 41 Journal of Theoretical Biology 36 Computers & Mathematics with Applications 32 Theoretical Population Biology 29 Nonlinear Analysis. Theory, Methods & Applications 28 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 25 Discrete and Continuous Dynamical Systems 24 Journal of Biological Dynamics 21 Calculus of Variations and Partial Differential Equations 20 Applicable Analysis 20 Applied Mathematics Letters 20 Abstract and Applied Analysis 18 Chaos, Solitons and Fractals 18 Journal of Dynamics and Differential Equations 17 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 17 Advances in Difference Equations 14 SIAM Journal on Applied Mathematics 13 Rocky Mountain Journal of Mathematics 13 Acta Applicandae Mathematicae 13 Nonlinear Dynamics 12 Communications in Nonlinear Science and Numerical Simulation 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Journal of Computational and Applied Mathematics 11 Journal of Functional Analysis 11 Proceedings of the American Mathematical Society 11 Mathematical Biosciences and Engineering 10 Mathematical Methods in the Applied Sciences 10 Applied Mathematical Modelling 9 Transactions of the American Mathematical Society 9 Physica D 9 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 9 Complexity 9 International Journal of Biomathematics 8 Mathematical and Computer Modelling 8 Journal of Applied Mathematics and Computing 8 Mathematical Modelling of Natural Phenomena 7 Discrete Dynamics in Nature and Society 7 Natural Resource Modeling 7 Journal of Applied Mathematics 7 Communications on Pure and Applied Analysis 7 Boundary Value Problems 6 Journal of Computational Physics 6 Ricerche di Matematica 6 European Journal of Applied Mathematics 6 Communications in Partial Differential Equations 6 Chaos 6 SIAM Journal on Applied Dynamical Systems 5 Applied Mathematics and Optimization 5 Applied Mathematics. Series B (English Edition) 5 Differential Equations and Dynamical Systems 5 Advanced Nonlinear Studies 5 Discrete and Continuous Dynamical Systems. Series S 4 Archive for Rational Mechanics and Analysis 4 Journal of Mathematical Physics 4 Nonlinearity 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Numerical Functional Analysis and Optimization 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Japan Journal of Industrial and Applied Mathematics 4 Journal of Nonlinear Science 4 Topological Methods in Nonlinear Analysis 4 Journal of Difference Equations and Applications 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Advances in Complex Systems 4 Frontiers of Mathematics in China 3 Bulletin of the Australian Mathematical Society 3 Memoirs of the American Mathematical Society 3 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 SIAM Journal on Mathematical Analysis 3 Computational and Applied Mathematics 3 Mathematical Problems in Engineering 3 Acta Mathematica Sinica. English Series 3 Journal of Biological Systems 3 The ANZIAM Journal 3 Science China. Mathematics 3 Journal of Function Spaces 2 Indian Journal of Pure & Applied Mathematics 2 Journal d’Analyse Mathématique 2 Journal of Statistical Physics 2 Physica A 2 Ukrainian Mathematical Journal 2 Czechoslovak Mathematical Journal 2 Duke Mathematical Journal 2 Mathematics and Computers in Simulation 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Results in Mathematics 2 Applied Mathematics and Mechanics. (English Edition) 2 Stochastic Analysis and Applications 2 Applied Numerical Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series ...and 116 more Serials
all top 5

#### Cited in 36 Fields

 1,091 Biology and other natural sciences (92-XX) 987 Partial differential equations (35-XX) 328 Ordinary differential equations (34-XX) 178 Dynamical systems and ergodic theory (37-XX) 78 Numerical analysis (65-XX) 65 Operator theory (47-XX) 64 Probability theory and stochastic processes (60-XX) 54 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 51 Calculus of variations and optimal control; optimization (49-XX) 36 Integral equations (45-XX) 29 Systems theory; control (93-XX) 22 Difference and functional equations (39-XX) 21 Global analysis, analysis on manifolds (58-XX) 15 Fluid mechanics (76-XX) 12 Statistical mechanics, structure of matter (82-XX) 10 Real functions (26-XX) 10 Statistics (62-XX) 5 Combinatorics (05-XX) 5 Functional analysis (46-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Computer science (68-XX) 4 Mechanics of deformable solids (74-XX) 3 Potential theory (31-XX) 3 Differential geometry (53-XX) 3 Mechanics of particles and systems (70-XX) 3 Operations research, mathematical programming (90-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Algebraic topology (55-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Convex and discrete geometry (52-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)