In this paper, the dynamics of a delayed phytoplankton-zooplankton model is considered. Taking the delay due to the gestation of zooplankton as param- eter, we describe the local Hopf bifurcation by center manifold th...In this paper, the dynamics of a delayed phytoplankton-zooplankton model is considered. Taking the delay due to the gestation of zooplankton as param- eter, we describe the local Hopf bifurcation by center manifold theorem and normal form, then we discuss the global existence of periodic solution. At last, some simulations are given to support our result.展开更多
In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transm...In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transmission is given.At last,some simulations are given to support our result.展开更多
We analysis Hopf bifurcation in a Monod-Haldane predator-prey model with three delays in this paper.Fixingτ1 andτ2 and takingτ3 as parameter,the direction and stability of Hopf bifurcation are studied by using cent...We analysis Hopf bifurcation in a Monod-Haldane predator-prey model with three delays in this paper.Fixingτ1 andτ2 and takingτ3 as parameter,the direction and stability of Hopf bifurcation are studied by using center manifold theorem and normal form.At last some simulations are given to support our results.展开更多
基金supported by the National Natural Science Foundations of China(No.11431008)NSF of Shanghai grant(No.15ZR1423700)
文摘In this paper, the dynamics of a delayed phytoplankton-zooplankton model is considered. Taking the delay due to the gestation of zooplankton as param- eter, we describe the local Hopf bifurcation by center manifold theorem and normal form, then we discuss the global existence of periodic solution. At last, some simulations are given to support our result.
文摘In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transmission is given.At last,some simulations are given to support our result.
文摘We analysis Hopf bifurcation in a Monod-Haldane predator-prey model with three delays in this paper.Fixingτ1 andτ2 and takingτ3 as parameter,the direction and stability of Hopf bifurcation are studied by using center manifold theorem and normal form.At last some simulations are given to support our results.
