Bifurcation Analysis Of A Diffusive Predator-Prey System

Abstract

For ecological systems, one of the main characters is the relationship between di er- ent species and their living environment. Thus modeling predator-prey interactions is one of the important issues in mathematical ecology. For the classical predator-prey models, the crucial components are the growth rate of prey species in the absence of predator, the mortality rate of predator species in the absence of prey and the functional response the predator to the prey. This thesis involves a di usive predator-prey system, in which the predator species Holling type II functional response and linear mortality rate. The stability of positive constant equilibrium, Hopf bifurcations, and di usion-driven Turing instability are investigated. The explicit condition for the occurrence of the di usion-driven Turing instability is derived. Finally, numerical simulations are carried out to verify and extend the theoretical results. As we observe the numerical result match the analytical result as expected. When we change the values of parameters the stability of equilibrium changed stable one become unstable and vice versa.