A Diffusive Ivlev-type Predator-prey System with Smith Growth and a Protection Zone

Abstract:

      This paper is concerned with a diffusive Ivlev-type predator-prey system with Smith growth and a protection zone. By discussing the existence and non-existence of positive solutions, we discover that the incorporation of the Smith growth function has enabled us to obtain a more precise criterion when judging the structure of bifurcation solutions, and determine a critical size for the protection zone. The results indicate that if the size of the protection zone is below the critical patch size, then the system has no positive steady state solution for excessively high intrinsic growth rates of predators. Conversely, if the size of the protection zone exceeds the critical patch size, there exists positive steady state solution regardless of how large the intrinsic growth rate of the predators is.