Multiplicity and stability of a predator-prey model with non-monotonic conversion rate

  • Nie H
  • Wu J
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Abstract

This paper is concerned with a predator-prey model possessing a non-monotonic conversion rate. The main purpose is to determine the multiple existence and stability of positive steady-state solutions to this system. The results show that if the parameter d is suitably large, then the system contains an S-shaped global bifurcation curve with respect to a bifurcation parameter. That is, the system has two or three positive solutions for a suitable range of parameters. Moreover, the stability of positive solutions on this curve is also given. If d is properly small, both uniqueness and non-uniqueness results can occur. The main tools used here include the bifurcation theory, the Lyapunov-Schmidt procedure, and the perturbation technique. © 2007 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Lyapunov-Schmidt procedure
  • Multiplicity
  • Perturbation technique
  • Stability

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