2020•Turkish Journal of ScienceOpen access

A note on Hopf bifurcation and steady state analysis for a predator-prey model

İrem Çay

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.

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Key concepts: Hopf bifurcation, Mathematics, Saddle-node bifurcation, Transcritical bifurcation, Period-doubling bifurcation, Biological applications of bifurcation theory, Pitchfork bifurcation, Bogdanov–Takens bifurcation