Stability of steady-state solutions to a prey–predator system with cross-diffusion☆

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Abstract

This paper is concerned with a cross-diffusion system arising in a prey–predator population model. The main purpose is to discuss the stability analysis for coexistence steady-state solutions obtained by Kuto and Yamada (J. Differential Equations, to appear). We will give some criteria on the stability of these coexistence steady states. Furthermore, we show that the Hopf bifurcation phenomenon occurs on the steady-state solution branch under some conditions.

MSC

35J65
35B35
92D25

Keywords

Cross diffusion
Steady-state solution
Stability
Hopf bifurcation
Lyapunov–Schmidt reduction

Cited by (0)

☆

This work was partially supported by JSPS Research Fellowships for Japanese Young Scientists (No. 05726).

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