Hopf bifurcation in a spatial predator-prey model with the square root functional response for the predator

Kazemi, Rasool; Asheghi, Rasoul

doi:10.22055/jamm.2023.41719.2076

Hopf bifurcation in a spatial predator-prey model with the square root functional response for the predator

Document Type : Original Paper

Authors

Rasool Kazemi ¹
Rasoul Asheghi ²

¹ Department of Mathematical Sciences, University of Kashan, Kashan, Iran, 87317-53153

² Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111

10.22055/jamm.2023.41719.2076

Abstract

‎In this paper‎, ‎we consider a diffusive predator-prey model‎, ‎in which the prey population lives in groups and has a social behavior‎. ‎We show that Hopf bifurcation and the existence of a center manifold may occur‎.

‎The linear stability analysis shows that a Hopf bifurcation occurs in the corresponding homogeneous system‎.

‎Next‎, ‎we study the effect of diffusion parameters on homogeneous dynamics‎.

‎By choosing a proper bifurcation parameter‎, ‎we prove that a Hopf bifurcation occurs in the nonhomogeneous system‎. ‎We compute the normal form of this bifurcation up to the third order and obtain the direction of the Hopf bifurcation‎. ‎Finally‎, ‎we provide numerical simulations to illustrate our analytical findings‎.

Highlights

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Keywords

Main Subjects

Dynamic Systems

References