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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
