Turing pattern selection in a reaction–diffusion epidemic model

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

中国物理B ›› 2011, Vol. 20 ›› Issue (7): 74702-074702.doi: 10.1088/1674-1056/20/7/074702

Turing pattern selection in a reaction–diffusion epidemic model

王玮明¹, 刘厚业¹, 蔡永丽¹, 李镇清²

(1)College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China; (2)State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, China

收稿日期:2011-01-08 修回日期:2011-02-25 出版日期:2011-07-15 发布日期:2011-07-15
基金资助:
Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y7080041).

Turing pattern selection in a reaction–diffusion epidemic model

Wang Wei-Ming(王玮明)^a)†, Liu Hou-Ye(刘厚业)^a), Cai Yong-Li (蔡永丽)^a), and Li Zhen-Qing (李镇清)^b)

^a College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China; ^b State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, China

Received:2011-01-08 Revised:2011-02-25 Online:2011-07-15 Published:2011-07-15
Supported by:
Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y7080041).

摘要/Abstract

摘要： 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 v, the sequence “H₀ hexagons → H₀-hexagon-stripe mixtures → stripes → H_π-hexagon-stripe mixtures → H_π hexagons” is observed. This may enrich the pattern dynamics in a diffusive epidemic model.

关键词: epidemic model, pattern selection, amplitude equations, Turing instability

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.

Key words: epidemic model, pattern selection, amplitude equations, Turing instability

中图分类号: (Pattern selection; pattern formation)

47.54.-r

87.23.Cc (Population dynamics and ecological pattern formation) 89.75.Kd (Patterns)

王玮明, 刘厚业, 蔡永丽, 李镇清. Turing pattern selection in a reaction–diffusion epidemic model[J]. 中国物理B, 2011, 20(7): 74702-074702.

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[J]. Chin. Phys. B, 2011, 20(7): 74702-074702.

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Turing pattern selection in a reaction–diffusion epidemic model

Turing pattern selection in a reaction–diffusion epidemic model

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