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Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems

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  • Jinglei Tian
  • Yongguang Yu
  • Hu Wang

Abstract

Two kinds of three-dimensional fractional Lotka-Volterra systems are discussed. For one system, the asymptotic stability of the equilibria is analyzed by providing some sufficient conditions. And bifurcation property is investigated by choosing the fractional order as the bifurcation parameter for the other system. In particular, the critical value of the fractional order is identified at which the Hopf bifurcation may occur. Furthermore, the numerical results are presented to verify the theoretical analysis.

Suggested Citation

  • Jinglei Tian & Yongguang Yu & Hu Wang, 2014. "Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, March.
    • Handle: RePEc:hin:jnlmpe:695871
    DOI: 10.1155/2014/695871
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    Cited by:

    1. Yang, Jing & Hou, Xiaorong & Li, Xiaoxue & Luo, Min, 2022. "A parameter space method for analyzing Hopf bifurcation of fractional-order nonlinear systems with multiple-parameter," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Huang, Chengdai & Cao, Jinde & Xiao, Min, 2016. "Hybrid control on bifurcation for a delayed fractional gene regulatory network," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 19-29.

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