Bifurcation analysis of a diffusive model of pioneer and climax species interaction
Tóm tắt
A diffusive model of pioneer and climax species interaction is considered. We perform a detailed Hopf bifurcation analysis to the model, and derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solutions.
Tài liệu tham khảo
Selgrade JF, Namkoong G: Stable periodic behavior in a pioneer-climax model. Natural Resource Modeling 1990, 4: 215-227.
Sumner S: Competing species models for pioneer-climax forest dynamical systems. Proc Dynam Syst Appl 1994, 1: 351-358.
Brown S, Dockery J, Pernarowski M: Traveling wave solutions of a reaction-diffusion model for competing pioneer and climax species. Math Biosci 2005, 194: 21-36. 10.1016/j.mbs.2004.10.001
Buchanan JR: Turing instability in pioneer/climax species interactions. Math Biosci 2005, 194: 199-216. 10.1016/j.mbs.2004.10.010
Yi F, Wei J, Shi J: Bifurcation and spatio-temporal patterns in a diffusivehomogenous predator-prey system. J Diff Equa 2009, 246: 1944-1977. 10.1016/j.jde.2008.10.024
Liu J, Yi F, Wei J: Multiple bifurcation analysis and spatiotemporal patterns in a 1-D Gierer-Meinhardt model of morphogenesis. Int J Bifurcation Chaos 2010, 20: 1007-1025. 10.1142/S0218127410026289