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Delay-Induced Oscillations in a Competitor-Competitor-Mutualist Lotka-Volterra Model

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  • Changjin Xu

Abstract

This paper deals with a competitor-competitor-mutualist Lotka-Volterra model. A series of sufficient criteria guaranteeing the stability and the occurrence of Hopf bifurcation for the model are obtained. Several concrete formulae determine the properties of bifurcating periodic solutions by applying the normal form theory and the center manifold principle. Computer simulations are given to support the theoretical predictions. At last, biological meaning and a conclusion are presented.

Suggested Citation

  • Changjin Xu, 2017. "Delay-Induced Oscillations in a Competitor-Competitor-Mutualist Lotka-Volterra Model," Complexity, Hindawi, vol. 2017, pages 1-12, April.
    • Handle: RePEc:hin:complx:2578043
    DOI: 10.1155/2017/2578043
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    References listed on IDEAS

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    1. Qiming Liu & Rui Xu, 2003. "Periodic solution for a delayed three-species food-chain system with Holling type-II functional response," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-14, January.
    2. Xu, Rui & Ma, Zhien, 2008. "Stability and Hopf bifurcation in a ratio-dependent predator–prey system with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 669-684.
    3. Yu, Chunbo & Wei, Junjie, 2009. "Stability and bifurcation analysis in a basic model of the immune response with delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1223-1234.
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    Cited by:

    1. Zizhen Zhang & Fangfang Yang & Wanjun Xia, 2019. "Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays," Complexity, Hindawi, vol. 2019, pages 1-17, November.
    2. Chuanjun Dai & Hengguo Yu & Qing Guo & He Liu & Qi Wang & Zengling Ma & Min Zhao, 2019. "Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-16, February.

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