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Dynamical behaviors of a partial-dependent predator–prey system

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  • Cheng, Zunshui
  • Lin, Yiping
  • Cao, Jinde

Abstract

In this paper, the dynamical behaviors are investigated for a partial-dependent predator–prey system with Holling type-II functional response. The change of equilibria number and their stability are discussed, and several sufficient conditions are given for checking existence of two positive steady states and the existence of limit cycle for the predator–prey system. In addition, their biological explanations are presented, and some numerical simulations are given to illustrate the effectiveness of the obtained results.

Suggested Citation

  • Cheng, Zunshui & Lin, Yiping & Cao, Jinde, 2006. "Dynamical behaviors of a partial-dependent predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 67-75.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:1:p:67-75
    DOI: 10.1016/j.chaos.2005.05.002
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    Cited by:

    1. Çelik, Canan & Duman, Oktay, 2009. "Allee effect in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1956-1962.
    2. Sun, Yeong-Jeu, 2009. "Existence of self-oscillation for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 731-734.
    3. Sun, Yeong-Jeu, 2007. "Limit cycles design for a class of bilinear control systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 156-162.
    4. Lv, Jian Cheng & Yi, Zhang, 2007. "Some chaotic behaviors in a MCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1040-1047.
    5. Sun, Yeong-Jeu, 2009. "The existence of the exponentially stable limit cycle for a class of nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2357-2362.
    6. Sun, Yeong-Jeu, 2008. "Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 89-96.

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