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2022 Hopf bifurcation in a diffusive predator-prey model with a square-root singularity
Rasoul Asheghi
Topol. Methods Nonlinear Anal. 59(1): 193-220 (2022). DOI: 10.12775/TMNA.2021.024

Abstract

In this paper, stability and Hopf bifurcation in a diffusive predator-prey system are discussed considering prey species' group behavior. The interaction term is of Holling type II with the prey density X under the square root. The local behavior is first discussed for the corresponding homogeneous system. Then, the diffusive system's linear stability is discussed around a homogeneous equilibrium state followed by bifurcations in the infinite-dimensional system. By the linear stability analysis, we see that a Hopf bifurcation occurs in the homogeneous system. By choosing a proper bifurcation parameter, we prove that a Hopf bifurcation occurs in the nonhomogeneous system. Furthermore, the direction of the Hopf bifurcation is obtained.

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Rasoul Asheghi. "Hopf bifurcation in a diffusive predator-prey model with a square-root singularity." Topol. Methods Nonlinear Anal. 59 (1) 193 - 220, 2022. https://doi.org/10.12775/TMNA.2021.024

Information

Published: 2022
First available in Project Euclid: 23 March 2022

Digital Object Identifier: 10.12775/TMNA.2021.024

Keywords: Hopf bifurcation , predator-prey model , reaction-diffusion system , square-root singularity

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.59 • No. 1 • 2022
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