A Note on Hopf Bifurcation and Steady State Analysis for a Predator-Prey Model

Abstract

This paper is concerned with the Hopf bifurcation and steady state analysis of a predator-prey model. Firstly, by analyzing the characteristic equation, the local stability of the nonnegative equilibriums is discussed. Then the Hopf bifurcation around the positive equilibrium is obtained, and the direction and the stability of the Hopf bifurcation are investigated. Finally, some numerical simulations are given to support the theoretical results.

Keywords

• Predator-prey model
• Steady state analysis
• Existence of Hopf bifurcation
• Supercritical bifurcation

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