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The study of a ratio-dependent predator–prey model with stage structure in the prey

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Abstract

In this paper, a ratio-dependent predator–prey model with stage structure in the prey is constructed and investigated. In the first part of this paper, some sufficient conditions for the existence and stability of three equilibriums are obtained. In the second part, we consider the effect of impulsive release of predator on the original system. A sufficient condition for the global asymptotical stability of the prey-eradication periodic solution is obtained. We also get the condition, under which the prey would never be eradicated, i.e., the impulsive system is permanent. At last, we give a brief discussion.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, 041004, People’s Republic of China

    Ruiqing Shi

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Ruiqing Shi & Lansun Chen

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  1. Ruiqing Shi
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  2. Lansun Chen
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Correspondence to Ruiqing Shi.

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Shi, R., Chen, L. The study of a ratio-dependent predator–prey model with stage structure in the prey. Nonlinear Dyn 58, 443–451 (2009). https://doi.org/10.1007/s11071-009-9491-2

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  • DOI: https://doi.org/10.1007/s11071-009-9491-2

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