Research On A Delay-induced Predator-prey System With Habitat Complexity

This paper,on the basis of the predator-prey system with Holling III functional response,intends to establish a predator-prey system with habitat complexity and multiple delays effects by incorporating the effect of habitat complexity,production delay and gestation delay into the considered system,and study the influence of habitat complexity and time-delay on the dynamic behavior of the predator system.In this paper,the dynamical behavior of the presented system is analyzed by using the theory of differential equation,including the boundedness and stability of equilibrium point,Hopf bifurcation as well as the existence of supercritical bifurcation.Furthermore,an explanation of the analysis results ecologically is given,which show that the habitat complexity has an positive influence on the density of the prey population,while has a negative influence on that of predators under a certain condition.Meanwhile,when the habitat complexity reaches a certain critical value,the coexistence equilibrium point of the system will be changed from unstable to stable.Next,the present author analyzes the dynamical consequences caused by time delay under three different circumstances.The existence of Hopf bifurcation and supercritical bifurcation are assessed respectively by applying the transversal condition and Sotomayor theorem.Finally,in order to further verify the theoretical results,the Matlab is applied to do numerical simulation in the system.The results show that the dynamic behaviors of considered system will be changed when the habitat complexity and the time delay reaches a certain critical value.