Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System

Qingsong Liu, Yiping Lin, Jingnan Cao and Jinde Cao

Discrete Dynamics in Nature and Society, 2014, vol. 2014, 1-7

Abstract:

The local reaction-diffusion Lengyel-Epstein system with delay is investigated. By choosing as bifurcating parameter, we show that Hopf bifurcations occur when time delay crosses a critical value. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are performed to support the analytical results and the chaotic behaviors are observed.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:139375

DOI: 10.1155/2014/139375

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