Title: Bifurcation analysis of a predator-prey model with volume-filling mechanism

Authors: Hui Hao; Yan Li; Fengrong Zhang; Zhiyi Lv

Addresses: College of Science, China University of Petroleum (East China), Huangdao, Qingdao, China ' College of Science, China University of Petroleum (East China), Huangdao, Qingdao, China ' College of Science, China University of Petroleum (East China), Huangdao, Qingdao, China ' College of Science, China University of Petroleum (East China), Huangdao, Qingdao, China

Abstract: In this paper, a predator-prey model with the tendency mechanism of volume-filling effect under homogeneous Neumann boundary conditions is studied. Firstly, in the case of predation tendency and spatial diffusion, the stability of non-negative equilibria is discussed by analysing the characteristic equation of the corresponding linearisation system. Secondly, by Hopf bifurcation theorem, the existence of periodic patterns is investigated. Next, we mainly study the steady state bifurcation when the parameter χ is selected. It is shown that the chemotactic mechanism has no effect on the existence of Hopf bifurcation when α is selected as a bifurcation parameter. Whereas, the parameter χ can induce the steady state bifurcation. Finally, to illustrate the theoretical analysis, numerical simulations are carried out.

Keywords: predator-prey model; stability; Hopf bifurcation; volume-filling; steady state bifurcation.

DOI: 10.1504/IJWMC.2023.134674

International Journal of Wireless and Mobile Computing, 2023 Vol.25 No.3, pp.272 - 281

Received: 29 Nov 2022
Accepted: 02 Mar 2023
Published online: 03 Nov 2023 *

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