On the effects of migration and spatial heterogeneity on single and multiple species

Journal of Differential Equations

Volumn 223, Issue 2, 2006, Pages 400-426

  Lou, Yuan ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645126043     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2005.05.010     Document Type: Article

References (38)

1. J.M. Arrieta A.N. Carvalho A. Rodriguez-Bernal Upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions J. Differential Equations 168 2000 33-59
2. R.S. Cantrell C. Cosner The effects of spatial heterogeneity in population dynamics J. Math. Biol. 29 1991 315-338
3. R.S. Cantrell C. Cosner Should a park be an island? SIAM J. Appl. Math. 53 1993 219-252
4. R.S. Cantrell C. Cosner On the effects of spatial heterogeneity on the persistence of interacting species J. Math. Biol. 37 1998 103-145
5. R.S. Cantrell, C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Series in Mathematical and Computational Biology, Wiley, Chichester, UK, 2003.
6. R.S. Cantrell C. Cosner V. Hutson Permanence in ecological systems with diffusion Proc. Roy. Soc. Edinburgh A 123 1993 553-559
7. R.S. Cantrell C. Cosner V. Hutson Ecological models, permanence and spatial heterogeneity Rocky Mount. J. Math. 26 1996 1-35
8. R.S. Cantrell C. Cosner Y. Lou Multiple reversals of competitive dominance in ecological reserves via external habitat degradation J. Dynam. Differential Equations 16 2004 973-1010
9. A.N. Carvalho J.K. Hale Large diffusion with dispersion Nonlinear Anal. 17 1991 1139-1151
10. E. Conway D. Hoff J. Smoller Large time behavior of solutions of systems of nonlinear reaction-diffusion equations SIAM J. Appl. Math. 35 1978 1-16
11. J. Dockery V. Hutson K. Mischaikow M. Pernarowski The evolution of slow dispersal rates a reaction-diffusion model J. Math. Biol. 37 1998 61-83
12. Y. Du Effects of a degeneracy in the competition model, Part I. Classical and generalized steady-state solutions J. Differential Equations 181 2002 92-132
13. Y. Du Effects of a degeneracy in the competition model, Part II. Perturbation and dynamical behavior J. Differential Equations 181 2002 133-164
14. Y. Du Realization of prescribed patterns in the competition model J. Differential Equations 193 2003 147-179
15. J.E. Furter J. López-Gómez Diffusion-mediated permanence problem for a heterogeneous Lotka-Volterra competition model Proc. Roy. Soc. Edinburgh 127A 1997 281-336
16. D. Gilbarg N. Trudinger Elliptic Partial Differential Equation of Second Order second ed. 1983 Springer Berlin
17. J.K. Hale Large diffusivity and asymptotic behavior in parabolic systems J. Math. Anal. Appl. 118 1986 455-466
18. A. Hastings Spatial heterogeneity and ecological models Ecology 71 1990 426-428
19. P. Hess Periodic Parabolic Boundary Value Problems and Positivity 1991 Longman Scientific & Technical Harlow, UK
20. E.E. Holmes M.A. Lewis J.E. Banks R.R. Veit Partial differential equations in ecology spatial interactions and population dynamics Ecology 75 1994 17-29
21. S. Hsu H. Smith P. Waltman Competitive exclusion and coexistence for competitive systems on ordered Banach spaces Trans. Amer. Math. Soc. 348 1996 4083-4094
22. V. Hutson, J. López-Gómez, K. Mischaikow, G. Vickers, Limit behavior for a competing species problem with diffusion, in Dynamical Systems and Applications, World Scientific Series Applicable Analysis, vol. 4, World Scientific, River Edge, NJ, 1995, pp. 501-533.
23. V. Hutson Y. Lou K. Mischaikow Spatial heterogeneity of resources versus Lotka-Volterra dynamics J. Differential Equations 185 2002 97-136
24. V. Hutson Y. Lou K. Mischaikow Convergence in competition models with small diffusion coefficients J. Differential Equations 211 2005 135-161
25. V. Hutson Y. Lou K. Mischaikow P. Poláčik Competing species near the degenerate limit SIAM J. Math. Anal. 35 2003 453-491
26. V. Hutson S. Martinez K. Mischaikow G.T. Vickers The evolution of dispersal J. Math. Biol. 47 2003 483-517
27. V. Hutson K. Mischaikow P. Poláčik The evolution of dispersal rates in a heterogeneous time-periodic environment J. Math. Biol. 43 2001 501-533
28. M. Iida M. Tatsuya H. Ninomiya E. Yanagida Diffusion-induced extinction of a superior species in a competition system Japan J. Iudust. Appl. Math. 15 1998 223-252
29. J. Jiang X. Liang X. Zhao Saddle point behavior for monotone semiflows and reaction-diffusion models J. Differential Equations 203 2004 313-330
30. J. López-Gómez, Coexistence and meta-coexistence for competing species, Houston J. Math. (2003) 483-536.
31. J.D. Murray, Mathematical Biology. II. Spatial Models and Biomedical Applications, third ed., Interdisciplinary Applied Mathematics, vol. 18, Springer, New York, 2003.
32. H. Ninomiya Separatrices of competition-diffusion equations J. Math. Kyoto Univ. 35 1995 539-567
33. A. Okubo, S. Levin, Diffusion and Ecological Problems: Modern Perspectives, second ed., Interdisciplinary Applied Mathematics, vol. 14, Springer, New York, 2001.
34. S. Pacala J. Roughgarden Spatial heterogeneity and interspecific competition Theor. Popul. Biol. 21 1982 92-113
35. C.V. Pao Nonlinear Parabolic and Elliptic Equations 1992 Plenum New York
36. A.B. Potapov, M.A. Lewis, Climate and competition: The effect of moving range boundaries on habitat invisibility, Bull. Math. Biol. (2004) 975-1008.
37. M.H. Protter H.F. Weinberger Maximum Principles in Differential Equations second ed. 1984 Springer Berlin
38. N. Shigesada, K. Kawasaki, Biological Invasions: Theory and Practice, Oxford Series in Ecology and Evolution, Oxford University Press, Oxford, New York, Tokyo, 1997.