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Bifurcation in a Discrete Competition System

Author

Listed:
  • Li Xu
  • Lianjun Zou
  • Zhongxiang Chang
  • Shanshan Lou
  • Xiangwei Peng
  • Guang Zhang

Abstract

A new difference system is induced from a differential competition system by different discrete methods. We give theoretical analysis for local bifurcation of the fixed points and derive the conditions under which the local bifurcations such as flip occur at the fixed points. Furthermore, one- and two-dimensional diffusion systems are given when diffusion terms are added. We provide the Turing instability conditions by linearization method and inner product technique for the diffusion system with periodic boundary conditions. A series of numerical simulations are performed that not only verify the theoretical analysis, but also display some interesting dynamics.

Suggested Citation

  • Li Xu & Lianjun Zou & Zhongxiang Chang & Shanshan Lou & Xiangwei Peng & Guang Zhang, 2014. "Bifurcation in a Discrete Competition System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-7, April.
    • Handle: RePEc:hin:jnddns:193143
    DOI: 10.1155/2014/193143
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    Cited by:

    1. Xu, Li & Liu, Jiayi & Zhang, Guang, 2018. "Pattern formation and parameter inversion for a discrete Lotka–Volterra cooperative system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 226-231.

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