The impact of fear effect on the dynamics of a delayed predator-prey model with stage structure  

作　　者：Qi Cao Guotai Chen Wensheng Yang 

机构地区：[1]School of Mathematics and Statistics Fujian Normal University,Fuzhou 350117 Fujian,P.R.China [2]FJKLMAA and Center for Applied Mathematics of Fujian Province(FJNU)Fuzhou350117,Fujian,P.R.China

出　　处：《International Journal of Biomathematics》2023年第8期263-296,共34页生物数学学报（英文版）

基　　金：supported by the Natural Science Foundation of China(11672074);the Natural Science Foundation of Fujian Province(2022J01192).

摘　　要：In this paper,a stage structure predator-prey model consisting of three nonlinear ordinary differential equations is proposed and analyzed.The prey populations are divided into two parts:juvenile prey and adult prey.From extensive experimental data,it has been found that prey fear of predators can alter the physiological behavior of individual prey,and the fear effect reduces their reproductive rate and increases their mortality.In addition,we also consider the presence of constant ratio refuge in adult prey populations.Moreover,we consider the existence of intraspecific competition between adult prey species and predator species separately in our model and also introduce the gestation delay of predators to obtain a more realistic and natural eco-dynamic behaviors.We study the positivity and boundedness of the solution of the non-delayed system and analyze the existence of various equilibria and the stability of the system at these equilibria.Next by choosing the intra-specific competition coeficient of adult prey as bifurcation parameter,we demonstrate that Hopf bifurcation may occur near the positive equilibrium point.Then by taking the gestation delay as bifurcation parameter,the suficient conditions for the existence of Hopf bifurcation of the delayed system at the positive equilibrium point are given.And the direction of Hopf bifurcation and the stability of the periodic solution are analyzed by using the center manifold theorem and normal form theory.What's more,numerical experiments are performed to test the theoretical results obtained in this paper.

关 键 词：Stage-structure model fear effect time delay Hopf bifurcation 

分 类 号：O175[理学—数学]