Turing Instability Of A Lotka-Volterra Food Chain Model With Ominivory

In this paper, we consider the stability of a Lotka-Volterra food chain model with omnivory. First, the stability of nonnegative constant equilibria in the corre-sponding ODE model is investigated; Second, the stability of nonnegative constant equilibria in the corresponding self-diffusion model is discussed, the resoult is proved that self-diffusion cannot led to Turing instability; Finally, the stability of nonneg-ative constant equilibria in the corresponding cross-diffusion model is investigat-ed. Through the stability analysis for the model, It is proved that cross-diffusion can lead to Turing instability when the cross-diffusion coefficient let enough large.