Pattern formation by super-diffusion in FitzHugh–Nagumo model

Naveed Iqbal, Ranchao Wu and Biao Liu

Applied Mathematics and Computation, 2017, vol. 313, issue C, 245-258

Abstract: The aim of this paper is to examine the Turing instability and pattern formation in the FitzHugh–Nagumo model with super-diffusion in two dimensional numerical simulation. We also studied the effects of the super-diffusive exponent on pattern formation concluding that with the presence of super-diffusion the stable homogenous steady state becomes unstable. By using the stability analysis of local equilibrium point, we procure the conditions which ensure that the Turing and Hopf bifurcations occur. For pattern selection, the weak nonlinear multi-scale analysis is used to derive the amplitude equations of the stationary patterns. We then apply amplitude equations and observe that this model has very rich dynamical behaviors, such as stripes, spots and hexagon patterns. The complexity of the dynamics in this system is theoretically discussed and graphically displayed in numerical simulation. The simulation helps us to show the effectiveness of theoretical analysis and patterns which appear numerically.

Keywords: Turing pattern; Fitzhugh–Nagumo model; Fractional Laplacian diffusion; Amplitude equation; Stability analysis (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317303843
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:313:y:2017:i:c:p:245-258

DOI: 10.1016/j.amc.2017.05.072

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().