In this paper,we consider a predator-prey system with modified Leslie-Gower and Holling type Ⅲ schemes.By regarding the time delay as the bifurcation parameter,the local asymptotic stability of the positive equilibri...In this paper,we consider a predator-prey system with modified Leslie-Gower and Holling type Ⅲ schemes.By regarding the time delay as the bifurcation parameter,the local asymptotic stability of the positive equilibrium is investigated.And we find that Hopf bifurcations can occur as the time delay crosses some critical values.In particular,special attention is paid to the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions.In addition,the global existence of periodic solutions bifurcating from the Hopf bifurcation are considered by applying a global Hopf bifurcation result.Finally,numerical simulations are carried out to illustrate the main theoretical results.展开更多
基金Supported by National Natural Science Foundation of China (61273070)Doctor Candidate Foundation of Jiangnan University (JUDCF12030)Anhui Provincial Natural Science Foundation (1208085QA11)
文摘In this paper,we consider a predator-prey system with modified Leslie-Gower and Holling type Ⅲ schemes.By regarding the time delay as the bifurcation parameter,the local asymptotic stability of the positive equilibrium is investigated.And we find that Hopf bifurcations can occur as the time delay crosses some critical values.In particular,special attention is paid to the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions.In addition,the global existence of periodic solutions bifurcating from the Hopf bifurcation are considered by applying a global Hopf bifurcation result.Finally,numerical simulations are carried out to illustrate the main theoretical results.
