Advection-mediated coexistence of competing species

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Volumn 137, Issue 3, 2007, Pages 497-518

  Cantrell, Robert Stephen ^a   Cosner, Chris ^a   Lou, Yuan ^b  

^a Department of Biology   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547354459     PISSN: 03082105     EISSN: 14737124     Source Type: Journal    
DOI: 10.1017/S0308210506000047     Document Type: Article

References (21)

1. F. Belgacem. Elliptic boundary value problems with indefinite weights: variational formulations of the principal eigenvalue and applications. Pitman Research Notes in Mathematics, vol. 368 (Longman, 1997).
2. F. Belgacem and C. Cosner. The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment. Can. Appl. Math. Q. 3 (1995), 379-397.
3. R. S. Cantrell and C. Cosner. Spatial ecology via reaction-diffusion equations. Wiley Series in Mathematical and Computational Biology (Wiley, 2003).
4. R. S. Cantrell, C. Cosner and Y. Lou. Multiple reversals of competitive dominance in ecological reserve via external habitat degradation. J. Dynam. Diff. Eqns 16 (2004), 973-1010.
5. R. S. Cantrell, C. Cosner and Y. Lou. Movement towards better environments and the evolution of rapid diffusion. Math. Biosci. 204 (2006), 199-214.
6. C. Cosner and Y. Lou. When does movement toward better environment benefit a population? J. Math. Analysis Applic. 277 (2003), 489-503.
7. E. N. Dancer. Positivity of maps and applications. In Topological nonlinear analysis: degree, singularity, and variations (ed. M. Matzeu and A. Vignoli). Progress in Nonlinear Differential Equations and Their Applications, vol. 15, pp. 303-340 (Birkhäuser, 1995).
8. E. N. Dancer and P. Hess. Stability of fixed points for order-preserving discrete-time dynamical systems. J. Reine Angew. Math. 419 (1991), 125-139.
9. J. Dockery, V. Hutson, K. Mischaikow and M. Pernarowski. The evolution of slow dispersal rates: a reaction-diffusion model. J. Math. Biol. 37 (1998), 61-83.
10. D. Gilbarg and N. Trudinger. Elliptic partial differential equations of second order, 2nd edn (Springer, 1983).
11. J. K. Hale and G. Raugel. Reaction-diffusion equation on thin domains. J. Math. Pures Appl. 71 (1992), 32-95.
12. P. Hess. Periodic-parabolic boundary value problems and positivity. Pitman Research Notes in Mathematics, vol. 247 (Longman, 1991).
13. M. W. Hirsch. Stability and convergence in strongly monotone dynamical systems. J. Reine Angew. Math. 383 (1988), 1-51.
14. M. W. Hirsch and H. L. Smith. Asymptotically stable equilibria for monotone semiflows. Discrete Contin. Dynam. Syst. 14 (2006), 385-398.
15. S. Hsu, H. Smith and P. Waltman. Competitive exclusion and coexistence for competitive systems on ordered Banach spaces. Trans. Am. Math. Soc. 348 (1996), 4083-4094.
16. V. Hutsou, J. López-Gómez, K. Mischaikow and G. Vickers. Limit behavior for a competing species problem with diffusion. In Dynamical systems and applications, World Scientific Series in Applied Analysis, vol. 4, pp. 343-358 (World Scientific, 1995).
17. V. Hutson, Y. Lou, K. Mischaikow and P. Poláčik. Competing species near a degenerate limit. SIAM J. Math. Analysis 35 (2003), 453-491.
18. Y. Lou and W. M. Ni. Diffusion, self-diffusion and cross-diffusion. J. Diff. Eqns 131 (1996), 79-131.
19. Y. Lou, S. Martínez and P. Poláčik. Loops and branches of coexistence states in a Lotka-Volterra competition model. J. Diff. Eqns 230 (2006), 720-742.
20. H. Matano. Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems. J. Fac. Sci. Univ. Tokyo 30 (1984), 645-673.
21. M. H. Protter and H. F. Weinberger. Maximum principles in differential equations, 2nd edn (Springer, 1984).