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Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays

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  • Zhang, Jia-Fang
  • Chen, Heshan

Abstract

This paper is concerned with a Lotka–Volterra competition system with spatio-temporal delays. By using the linearization method, we show the local asymptotic behavior of the nonnegative steady-state solutions. Especially, the global asymptotic stability of the positive steady-state solution is investigated by the method of upper and lower solutions. The result of global asymptotic stability implies that the system has no nonconstant positive steady-state solution.

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  • Zhang, Jia-Fang & Chen, Heshan, 2014. "Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 69-75.
    • Handle: RePEc:eee:chsofr:v:61:y:2014:i:c:p:69-75
    DOI: 10.1016/j.chaos.2014.03.001
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    References listed on IDEAS

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    1. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    2. Huo, Hai-Feng & Li, Wan-Tong & Nieto, Juan J., 2007. "Periodic solutions of delayed predator–prey model with the Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 505-512.
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    Cited by:

    1. Wen, Zijuan & Fu, Shengmao, 2016. "Turing instability for a competitor-competitor-mutualist model with nonlinear cross-diffusion effects," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 379-385.

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