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Bifurcation analysis of a diffusive predator-prey model with Beddington-DeAngelis functional response
Qiannan Song,Ruizhi Yang,Chunrui Zhang,Lei Wang
Keywords:Predator-prey; Turing instability; Hopf bifurcation; Turing-Hopf bifurcation
Abstract:
      In this paper, we consider a diffusive predator-prey model with Beddington-DeAngelis functional response. The Turing instability and Hopf bifurcation of the coexisting equilibrium are investigated. We also use bifurcation parameters m, d2 to study the Turing-Hopf bifurcation. In addition, we compute the normal form for the Turing-Hopf bifurcation. On the basis of the corresponding normal form, there exists complex spatiotemporal dynamics near Turing-Hopf bifurcation point. Finally, Some numerical simulations are given to illustrate our theoretical results.