Reversing invasion in bistable systems

Journal of Mathematical Biology

Volumn 65, Issue 6-7, 2012, Pages 1101-1124

  Alzahrani, Ebraheem O ^a   Davidson, Fordyce A ^a   Dodds, Niall ^a  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

Bistable; Competition; Reaction diffusion; Wave speed

Indexed keywords

EID: 84869179947     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-011-0490-9     Document Type: Article

References (19)

1. Alzahrani EO, Davidson FA, Dodds N (2010) Travelling waves in near-degenerate bistable competition models. Math Model Nat Phenom 5(5): 13-35.
2. Cantrell RS, Cosner C (2003) Spatial ecology via reaction-diffusion equations. John Wiley and Sons Ltd, New York.
3. Crooks E (2010) Front profiles in the vanishing-diffusion limit for monostable reaction-diffusion-convection equations. Differ Integr Equ 23(5-6): 495-512.
4. Evans L (1998) Partial differential equations, graduate studies in mathematics, vol 19. American Mathematical Society, Providence.
5. Fang J, Zhao X (2009) Monotone wavefronts for partially degenerate reaction-diffusion systems. J Dyn Differ Equ 21(4): 663-680.
6. Grindrod P (1996) The theory and applications of reaction-diffusion equations: patterns and waves. Clarendon Press, Oxford.
7. Heinze S, Schweizer B (2005) Creeping fronts in degenerate reaction-diffusion systems. Nonlinearity 18(6): 2455-2476.
8. Heinze S, Schweizer B, Schwetlick H (2004) Existence of front solutions in degenerate reaction diffusion systems. (Preprint 2004-03, SFB 359).
9. Hosono Y (1989) Singular perturbation analysis of travelling waves for diffusive Lotka-Volterra competition models. IMACS Ann Comput Appl Math (2: 687-692.
10. Hosono Y, Mimura M (1982) Singular perturbation approach to traveling waves in competing and diffusing species models. J Math Kyoto University 22(3): 435-461.
11. Lewis MA, Li B, Weinberger H (2002) Spreading speed and the linear determinacy for two-species competition models. J Math Biol 45: 219-233.
12. Li B, Weinberger H, Lewis MA (2005) Spreading speeds as slowest wave speeds for cooperative systems. Math Biosci 196: 82-98.
13. Murray J (2003) Mathematical biology, II: spatial models and biomedical applications, vol 2. Springer, Berlin.
14. Okubo A, Levin S (2001) Diffusion and ecological problems: modern perspectives. Springer, New York.
15. Owen M, Lewis M (2001) How predation can slow, stop or reverse a prey invasion. Bull Math Biol 63(4): 655-684.
16. Smoller J (1994) Shock waves and reaction-diffusion equations. Springer, Berlin.
17. Volpert A, Volpert V, Volpert V (1994) Traveling wave solutions of parabolic systems: translations of mathematical monographs, vol 140. American Mathematical Society, Providence.
18. Volpert V, Petrovskii S (2009) Reaction-diffusion waves in biology. Phys Life Rev 6(4): 267-310.
19. Weinberger H, Lewis MA, Li B (2002) Analysis of linear determinacy for spread in cooperative models. J Math Biol 45: 183-218.