Simple diffusion can support the pitchfork, the flip bifurcations, and the chaos
| Autor: | Lili Meng, Guang Zhang, Xinfu Li |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Period-doubling bifurcation
Numerical Analysis Applied Mathematics 010102 general mathematics Saddle-node bifurcation Lyapunov exponent 01 natural sciences Biological applications of bifurcation theory 010305 fluids & plasmas Nonlinear Sciences::Chaotic Dynamics symbols.namesake Maximum principle Pitchfork bifurcation Control theory Modeling and Simulation 0103 physical sciences symbols Applied mathematics 0101 mathematics Bifurcation Center manifold Mathematics |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 53:202-212 |
| ISSN: | 1007-5704 |
| Popis: | In this paper, a discrete rational fration population model with the Dirichlet boundary conditions will be considered. According to the discrete maximum principle and the sub- and supper-solution method, the necessary and sufficient conditions of uniqueness and existence of positive steady state solutions will be obtained. In addition, the dynamical behavior of a special two patch metapopulation model is investigated by using the bifurcation method, the center manifold theory, the bifurcation diagrams and the largest Lyapunov exponent. The results show that there exist the pitchfork, the flip bifurcations, and the chaos. Clearly, these phenomena are caused by the simple diffusion. The theoretical analysis of chaos is very imortant, unfortunately, there is not any results in this hand. However, some open problems are given. |
| Databáze: | OpenAIRE |
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