Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
Math. Model. Nat. Phenom., 1 1 (2006) 63-80
Published online: 2008-05-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Modulated traveling fronts for a nonlocal Fisher-KPP equation: A dynamical systems approach
Grégory Faye and Matt HolzerJournal of Differential Equations 258 (7) 2257 (2015)
https://doi.org/10.1016/j.jde.2014.12.006
Parabolic Equations in Biology
Benoît PerthameLecture Notes on Mathematical Modelling in the Life Sciences, Parabolic Equations in Biology 117 (2015)
https://doi.org/10.1007/978-3-319-19500-1_7
Basic stage structure measure valued evolutionary game model
John ClevelandMathematical Biosciences and Engineering 12 (2) 291 (2015)
https://doi.org/10.3934/mbe.2015.12.291
How morphology of artificial organisms influences their evolution
N. Bessonov, N. Reinberg and V. VolpertEcological Complexity 24 57 (2015)
https://doi.org/10.1016/j.ecocom.2015.09.005
Patterns for Competing Populations with Species Specific Nonlocal Coupling
A. Bayliss, V. A. Volpert, M. Alfaro, et al.Mathematical Modelling of Natural Phenomena 10 (6) 30 (2015)
https://doi.org/10.1051/mmnp/201510604
Spatial patterns of competing random walkers
Emilio Hernández-García, Els Heinsalu and Cristóbal LópezEcological Complexity 21 166 (2015)
https://doi.org/10.1016/j.ecocom.2014.06.005
Bistable travelling waves for nonlocal reaction diffusion equations
Matthieu Alfaro, Jérôme Coville and Gaël RaoulDiscrete & Continuous Dynamical Systems - A 34 (5) 1775 (2014)
https://doi.org/10.3934/dcds.2014.34.1775
Self-localized states in species competition
Pavel V. Paulau, Damià Gomila, Cristóbal López and Emilio Hernández-GarcíaPhysical Review E 89 (3) (2014)
https://doi.org/10.1103/PhysRevE.89.032724
On the nonlocal Fisher–KPP equation: steady states, spreading speed and global bounds
François Hamel and Lenya RyzhikNonlinearity 27 (11) 2735 (2014)
https://doi.org/10.1088/0951-7715/27/11/2735
Asymptotic behaviour of travelling waves for the delayed Fisher–KPP equation
Arnaud Ducrot and Grégoire NadinJournal of Differential Equations 256 (9) 3115 (2014)
https://doi.org/10.1016/j.jde.2014.01.033
Mathematics of Darwin’s Diagram
N. Bessonov, N. Reinberg, V. Volpert and A. MorozovMathematical Modelling of Natural Phenomena 9 (3) 5 (2014)
https://doi.org/10.1051/mmnp/20149302
Pattern formation in a model of competing populations with nonlocal interactions
B.L. Segal, V.A. Volpert and A. BaylissPhysica D: Nonlinear Phenomena 253 12 (2013)
https://doi.org/10.1016/j.physd.2013.02.006
Dispersal, Individual Movement and Spatial Ecology
Vitaly Volpert and Vitali VougalterLecture Notes in Mathematics, Dispersal, Individual Movement and Spatial Ecology 2071 331 (2013)
https://doi.org/10.1007/978-3-642-35497-7_12
Stability and pattern formation for competing populations with asymmetric nonlocal coupling
M.C. Tanzy, V.A. Volpert, A. Bayliss and M.E. NehrkornMathematical Biosciences 246 (1) 14 (2013)
https://doi.org/10.1016/j.mbs.2013.09.002
A relaxation method for one dimensional traveling waves of singular and nonlocal equations
Weiran Sun and Min TangDiscrete & Continuous Dynamical Systems - B 18 (5) 1459 (2013)
https://doi.org/10.3934/dcdsb.2013.18.1459
Social-ecological systems as complex adaptive systems: modeling and policy implications
Simon Levin, Tasos Xepapadeas, Anne-Sophie Crépin, et al.Environment and Development Economics 18 (2) 111 (2013)
https://doi.org/10.1017/S1355770X12000460
Evolutionary game theory on measure spaces: Well-posedness
John Cleveland and Azmy S. AcklehNonlinear Analysis: Real World Applications 14 (1) 785 (2013)
https://doi.org/10.1016/j.nonrwa.2012.08.002
Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait
Matthieu Alfaro, Jérôme Coville and Gaël RaoulCommunications in Partial Differential Equations 38 (12) 2126 (2013)
https://doi.org/10.1080/03605302.2013.828069
Analysis of meshless local radial point interpolation (MLRPI) on a nonlinear partial integro-differential equation arising in population dynamics
Elyas ShivanianEngineering Analysis with Boundary Elements 37 (12) 1693 (2013)
https://doi.org/10.1016/j.enganabound.2013.10.002
An efficient pseudo‐spectral Legendre–Galerkin method for solving a nonlinear partial integro‐differential equation arising in population dynamics
Farhad Fakhar‐Izadi and Mehdi DehghanMathematical Methods in the Applied Sciences 36 (12) 1485 (2013)
https://doi.org/10.1002/mma.2698
Evolutionary branching patterns in predator-prey structured populations
Marcello Delitala and Tommaso LorenziDiscrete & Continuous Dynamical Systems - B 18 (9) 2267 (2013)
https://doi.org/10.3934/dcdsb.2013.18.2267
Evolution of species trait through resource competition
Sepideh Mirrahimi, Benoît Perthame and Joe Yuichiro WakanoJournal of Mathematical Biology 64 (7) 1189 (2012)
https://doi.org/10.1007/s00285-011-0447-z
Generalized Transition Waves and Their Properties
Henri Berestycki and François HamelCommunications on Pure and Applied Mathematics 65 (5) 592 (2012)
https://doi.org/10.1002/cpa.21389
Rapid traveling waves in the nonlocal Fisher equation connect two unstable states
Matthieu Alfaro and Jérôme CovilleApplied Mathematics Letters 25 (12) 2095 (2012)
https://doi.org/10.1016/j.aml.2012.05.006
Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect
Shanshan Chen and Junping ShiJournal of Differential Equations 253 (12) 3440 (2012)
https://doi.org/10.1016/j.jde.2012.08.031
Properness and Topological Degree for Nonlocal Reaction‐Diffusion Operators
N. Apreutesei, V. Volpert and Nobuyuki KenmochiAbstract and Applied Analysis 2011 (1) (2011)
https://doi.org/10.1155/2011/629692
On selection dynamics for competitive interactions
Pierre-Emmanuel Jabin and Gaël RaoulJournal of Mathematical Biology 63 (3) 493 (2011)
https://doi.org/10.1007/s00285-010-0370-8
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
Alexander Lorz, Sepideh Mirrahimi and Benoît PerthameCommunications in Partial Differential Equations 36 (6) 1071 (2011)
https://doi.org/10.1080/03605302.2010.538784
Spectrum of some integro-differential operators and stability of travelling waves
A. Ducrot, M. Marion and V. VolpertNonlinear Analysis: Theory, Methods & Applications 74 (13) 4455 (2011)
https://doi.org/10.1016/j.na.2011.04.009
Feedback Stabilization for a Reaction-Diffusion System with Nonlocal Reaction Term
Sebastian Aniţa, Viorel Arnăutu and Smaranda DodeaNumerical Functional Analysis and Optimization 32 (4) 351 (2011)
https://doi.org/10.1080/01630563.2010.542266
Some remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains
Arnaud Ducrot, Vincent Guyonne and Michel LanglaisDiscrete & Continuous Dynamical Systems - S 4 (1) 67 (2011)
https://doi.org/10.3934/dcdss.2011.4.67
Stationary periodic and homoclinic solutions for nonlocal reaction-diffusion equations
Shangbing AiApplicable Analysis 89 (7) 963 (2010)
https://doi.org/10.1080/00036810903393791
Existence of Waves for a Nonlocal Reaction-Diffusion Equation
I. Demin and V. VolpertMathematical Modelling of Natural Phenomena 5 (5) 80 (2010)
https://doi.org/10.1051/mmnp/20105506
Existence and Asymptotic Properties of Solutions of a Nonlocal Evolution Equation Modeling Cell-Cell Adhesion
Janet Dyson, Stephen A. Gourley, Rosanna Villella-Bressan and Glenn F. WebbSIAM Journal on Mathematical Analysis 42 (4) 1784 (2010)
https://doi.org/10.1137/090765663
Modeling complex systems
Anastasios XepapadeasAgricultural Economics 41 (s1) 181 (2010)
https://doi.org/10.1111/j.1574-0862.2010.00499.x
Dispersal in a Statistically Structured Population: Fat Tails Revisited
Sergei Petrovskii and Andrew MorozovThe American Naturalist 173 (2) 278 (2009)
https://doi.org/10.1086/595755