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Stability of steady-state solutions to a prey–predator system with cross-diffusion. (English) Zbl 1210.35122
The author investigates a Lotka-Volterra prey-predator model with cross-diffusion effects. The stability of the coexistence steady-states is studied. Criteria on the stability of the coexistence steady-states are obtained. The author proves that the Hopf bifurcation phenomenon on steady-states occurs under certain conditions.
MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
35B35Stability of solutions of PDE
92D25Population dynamics (general)