Spatiotemporal Dynamics in a Predator–Prey Model with Functional Response Increasing in Both Predator and Prey Densities

Ruizhi Yang, Qiannan Song and Yong An
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Ruizhi Yang: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Qiannan Song: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Yong An: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Mathematics, 2021, vol. 10, issue 1, 1-15

Abstract: In this paper, a diffusive predator–prey system with a functional response that increases in both predator and prey densities is considered. By analyzing the characteristic roots of the partial differential equation system, the Turing instability and Hopf bifurcation are studied. In order to consider the dynamics of the model where the Turing bifurcation curve and the Hopf bifurcation curve intersect, we chose the diffusion coefficients d 1 and β as bifurcating parameters. In particular, the normal form of Turing–Hopf bifurcation was calculated so that we could obtain the phase diagram. For parameters in each region of the phase diagram, there are different types of solutions, and their dynamic properties are extremely rich. In this study, we have used some numerical simulations in order to confirm these ideas.

Keywords: predator–prey model; Turing–Hopf bifurcation; Hopf bifurcation; Turing instability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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