Turing pattern selection in a reaction–diffusion epidemic model

doi:10.1088/1674-1056/20/7/074702

Abstract We present Turing pattern selection in a reaction--diffusion epidemic model under zero-flux boundary conditions. The value of this study is twofold. First, it establishes the amplitude equations for the excited modes, which determines the stability of amplitudes towards uniform and inhomogeneous perturbations. Second, it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication: on increasing the control parameter $\nu$, the sequence ``$H_0$ hexagons $\rightarrow$ $H_0$-hexagon-stripe mixtures $\rightarrow$ stripes $\rightarrow$ $H_{\pi}$-hexagon-stripe mixtures $\rightarrow$ $H_{\pi}$ hexagons" is observed. This may enrich the pattern dynamics in a diffusive epidemic model.

Keywords: epidemic model pattern selection amplitude equations Turing instability

Received: 08 January 2011
Revised: 25 February 2011
Accepted manuscript online:

PACS:	47.54.-r	(Pattern selection; pattern formation)
	87.23.Cc	(Population dynamics and ecological pattern formation)
	89.75.Kd	(Patterns)

Fund: Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y7080041).

Cite this article:

Wang Wei-Ming(王玮明), Liu Hou-Ye(刘厚业), Cai Yong-Li (蔡永丽), and Li Zhen-Qing (李镇清) Turing pattern selection in a reaction–diffusion epidemic model 2011 Chin. Phys. B 20 074702

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Turing pattern selection in a reaction–diffusion epidemic model

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