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**Multiple positive periodic solutions for a generalized predator-prey system with exploited terms.**
*(English)*
Zbl 1145.34051

The authors consider a delayed periodic generalized predator-prey system with multiple exploited terms. The system models the dynamics of two predators for a prey and the delay is due to gestation. Sufficient conditions are given to guarantee that the system admits at least eight positive periodic solutions. The main result is established by employing the continuation theorem of coincidence degree theory.

Reviewer: Yuming Chen (Waterloo)

### MSC:

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

34K13 | Periodic solutions to functional-differential equations |

92D25 | Population dynamics (general) |

47N20 | Applications of operator theory to differential and integral equations |

### Keywords:

Positive periodic solution; generalized predator-prey system; continuation theorem; coincidence degree theory; delay; exploited term
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\textit{Z. Zhang} and \textit{T. Tian}, Nonlinear Anal., Real World Appl. 9, No. 1, 26--39 (2008; Zbl 1145.34051)

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### References:

[1] | Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Springer: Springer Berlin · Zbl 0339.47031 |

[2] | Ma, Z. E., Mathematical Modeling and Studying on Species Ecology (1996), Education Press: Education Press Hefei, (in Chinese) |

[4] | Tian, D. S.; Zeng, X. W., Existence of at least two periodic solutions of a ratio-dependent predator-prey model with exploited term, Acta Math. Appl. Sin. English Series, 21, 3, 489-494 (2005) · Zbl 1098.92072 |

[5] | Zhang, Z. Q.; Wang, H. L., Existence and global attractivity of a positive periodic solution for a generalized prey-predator system with time delay, Math. Comput. Modeling, 44, 188-203 (2006) · Zbl 1160.34066 |

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