Turing Instability Of A Three Species Food Chain Cross-diffusion Model

In this dissertation,the Turing instability of a three species food chain cross-diffusion model is discussed in detail.It is shown that if the top-predator only preys on the secondary predator,neither the reaction-diffusion nor SKT cross-diffusion system can change the stability of this model,but it can be changed by the lin-ear cross-diffusion rate.Furthermore,we also prove that when the top-predator consumes the predator and the prey species,the self-diffusion can not cause the change of stability in this model,but the large cross-diffusion rates play the role of destabilization effect in this model,that is,it can cause the phenomenon of Turing instability.