Analysis of Steady State for Variable-Territory Model with Limited Self-Limitation

This paper is concerned with a Variable-territory model with limited self-limitation of predator. By the bifurcation theorem, regular perturbation theorem and numerical simulation, the conditions of existence, stability and convergence of positive solutions are established. This work shows that prey and predator can be controlled by parameters in Variable-territory model, such as intrinsic growth rate, death rate, handling time and the self-limitation of predator.