Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10345051 | Computers & Mathematics with Applications | 2015 | 16 Pages |
Abstract
In this paper, we investigate the effect of diffusion on pattern formation in FitzHugh-Nagumo model. Through the linear stability analysis of local equilibrium we obtain the condition how the Turing bifurcation, Hopf bifurcation and the oscillatory instability boundaries arise. By using the method of the weak nonlinear multiple scales analysis and Taylor series expansion, we derive the amplitude equations of the stationary patterns. The analysis of amplitude equations shows the occurrence of different complex phenomena, including Turing instability Eckhaus instability and zigzag instability. In addition, we apply this analysis to FitzHugh-Nagumo model and find that this model has very rich dynamical behaviors, such as spotted, stripe and hexagon patterns. Finally, the numerical simulation shows that the analytical results agree with numerical simulation.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Qianqian Zheng, Jianwei Shen,