Turing instability in a Lotka-Volterra predator-prey model with cross-diffusion and harvesting rate. (Chinese. English summary) Zbl 1438.35034
Summary: In this paper, the Turing instability of a Lotka-Volterra predator-prey model with cross-diffusion and harvesting rate is discussed. It is proved that neither linear self-diffusion nor nonlinear SKT self-diffusion can change the stability of this model, but Turing pattern exists in the linear cross-diffusion and SKT cross-diffusion systems. Meanwhile, to illustrate the analysis results, some numerical examples are also included.
MSC:
35B35 | Stability in context of PDEs |
35K57 | Reaction-diffusion equations |
92D25 | Population dynamics (general) |