Turing Instability Of A Tritrophic Chain Model With Cross-diffusion

In this dissertation,we consider the Turing instability of a tritrophic chain model with cross-diffusion.First,we discuss the stability of nonnegative constant equilibria in the corresponding ODE model;Second,the stability of nonnegative constant equilibria in the corresponding semilinear reaction-diffusion model is investigated.It is shown that the generic linear self-diffusion can not change Turing instability;Finally,the stability of nonnegative constant equilibria in the cross-diffusion model is studied.Through this stability analysis,we find that this model will cause Turing instability phenomenon when cross-diffusion coefficient is large sufficiently.