Stability and Hopf bifurcation of a diffusive predator–prey model with predator saturation and competition

Abstract

This article discusses a predator–prey system with predator saturation and competition functional response. The local stability, existence of a Hopf bifurcation at the coexistence equilibrium and stability of bifurcating periodic solutions are obtained in the absence of diffusion. Further, we discuss the diffusion-driven instability, Hopf bifurcation for corresponding diffusion system with zero flux boundary condition and Turing instability region regarding the parameters are established. Finally, numerical simulations supporting the theoretical analysis are also included.

Keywords:

• stability analysis
• Hopf bifurcation
• predator–prey model
• Turing instability

AMS Subject Classifications::

• 35K57
• 92D25
• 70K50
• 34D20

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Erratum

Acknowledgements

The work of the second author is supported by Council of Scientific and Industrial Research, India (Grant No. 09/472(0143)/2010-EMR-I). The authors thank the referees for their constructive suggestions on improving the presentation of this article.