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Multiple periodic solutions of a ratio-dependent predator–prey model

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  • Xia, Yonghui
  • Han, Maoan

Abstract

A delayed ratio-dependent predator–prey model with non-monotone functional response is investigated in this paper. Some new and interesting sufficient conditions are obtained for the global existence of multiple positive periodic solutions of the ratio-dependent model. Our method is based on Mawhin’s coincidence degree and some estimation techniques for the a priori bounds of unknown solutions to the equation Lx=λNx. An example is represented to illustrate the feasibility of our main result.

Suggested Citation

  • Xia, Yonghui & Han, Maoan, 2009. "Multiple periodic solutions of a ratio-dependent predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1100-1108.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1100-1108
    DOI: 10.1016/j.chaos.2007.04.028
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    References listed on IDEAS

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    1. Hai-Feng Huo & Wan-Tong Li, 2003. "Existence and global stability of positive periodic solutions of a discrete delay competition system," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-13, January.
    2. Ma, Wen-Xiu & Maruno, Ken-ichi, 2004. "Complexiton solutions of the Toda lattice equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 219-237.
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