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

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  • Qingsong Liu
  • Yiping Lin
  • Jingnan Cao
  • Jinde Cao

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.

Suggested Citation

  • Qingsong Liu & Yiping Lin & Jingnan Cao & Jinde Cao, 2014. "Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnddns:139375
    DOI: 10.1155/2014/139375
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    References listed on IDEAS

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    1. Li, Kai & Wei, Junjie, 2009. "Stability and Hopf bifurcation analysis of a prey–predator system with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2606-2613.
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