期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 70, 期 5, 页码 1082-1097出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2015.06.031
关键词
Pattern formation; FitzHugh-Nagumo model; Turing-Hopf bifurcation; Amplitude equation; Secondary bifurcation; Stability analysis
资金
- National Natural Science Foundation of China [11272277]
- Innovation Scientists and Technicians Troop Construction Projects of Henan Province [134100510013]
- Innovative Research Team in University of Henan Province [13IRTSTHN019]
- International Cultivation of Henan Advanced Talents [201419]
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. (C) 2015 Elsevier Ltd. All rights reserved.
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