Effect Of A Protection Zone On A Diffusive Predator-Prey System With Ivlev-Type Functional Response

In this paper,two kinds of predator-prey models with Ivlev type functional response function and a protection zone are studied by the local and global bifur-cation theory,the principle of parabolic equation.The main works are summarized as follows:(1)The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcation theory.It is shown that the protection zone for prey has beneficial effects on the coexistence of the two species when the growth rate of predator is positive.Moreover,we examine the dependence of the coexistence region on the efficiency of the predator capture of the prey and the protection zone.(2)The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response and a strong Allee effect is considered.A critical patch size of protection zone is obtained.If the protection zone is over the critical patch size and the Allee effect threshold value b is small(0<b<1/2),then the over exploitation phenomenon can be avoided.If the protection zone is below the critical patch size or Allee effect threshold value b is large(1/2<b<1),then the over exploitation phenomenon still exists.Moreover,the two species can coexist in heterogeneous distribution when the protection zone is suitable.