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Traveling waves in a diffusive predator–prey system of Holling type: Point-to-point and point-to-periodic heteroclinic orbits

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  • Wu, Chufen
  • Yang, Yong
  • Weng, Peixuan

Abstract

We demonstrate the existence of small amplitude traveling wave train solutions and two kinds of traveling wave solutions of a diffusive predator–prey system with general Holling type functional response, i.e., the analysis shows the existence of periodic orbits, point-to-point connection and point-to-periodic orbit connection. Also, the minimal wave speed for biological invasion is obtained. The method or techniques used here can be extended to a diffusive predator–prey system with more general functional response, not only the Holling type.

Suggested Citation

  • Wu, Chufen & Yang, Yong & Weng, Peixuan, 2013. "Traveling waves in a diffusive predator–prey system of Holling type: Point-to-point and point-to-periodic heteroclinic orbits," Chaos, Solitons & Fractals, Elsevier, vol. 48(C), pages 43-53.
    • Handle: RePEc:eee:chsofr:v:48:y:2013:i:c:p:43-53
    DOI: 10.1016/j.chaos.2013.01.003
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    References listed on IDEAS

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    1. Jiang, Guirong & Lu, Qishao & Qian, Linning, 2007. "Complex dynamics of a Holling type II prey–predator system with state feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 448-461.
    2. Li, Wan-Tong & Wu, Shi-Liang, 2008. "Traveling waves in a diffusive predator–prey model with holling type-III functional response," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 476-486.
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