Versal unfoldings of predator-prey systems with ratio-dependent functional response |
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Authors: | Shigui Ruan Yilei Tang |
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Institution: | a Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA b Department of Mathematics, Shanghai Jiao Tong University, Minhang, Shanghai 200240, PR China c Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China |
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Abstract: | In this paper we study the versal unfolding of a predator-prey system with ratio-dependent functional response near a degenerate equilibrium in order to obtain all possible phase portraits for its perturbations. We first construct the unfolding and prove its versality and degeneracy of codimension 2. Then we discuss all its possible bifurcations, including transcritical bifurcation, Hopf bifurcation, and heteroclinic bifurcation, give conditions of parameters for the appearance of closed orbits and heteroclinic loops, and describe the bifurcation curves. Phase portraits for all possible cases are presented. |
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Keywords: | 34C05 34C60 92D25 |
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