In this paper,we study the effects of the nonlocal competition and double Allee effect in prey on a diffusive predator–prey model.We investigate the local stability of coexistence equilibrium in the predator–prey mo...In this paper,we study the effects of the nonlocal competition and double Allee effect in prey on a diffusive predator–prey model.We investigate the local stability of coexistence equilibrium in the predator–prey model by analyzing the eigenvalue spectrum.We study the consequence of double Allee effect on the prey population.Also,we discuss the existence of Hopf bifurcation under different parameters by using the gestation time delay of predators as a bifurcation parameter and analyzing the distribution of eigenvalues.By utilizing the normal form method and center manifold theorem,we have given some conditions that could determine the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions.Through our research,we obtain that the double Allee effect can affect the coexistence of prey and predator and induce periodic oscillations of the densities of prey and predator.In addition,the nonlocal competition can also affect the stability and homogeneity of the solutions,but may receive the consequences of the Allee effect as well as time delay.In the numerical simulation part,we further demonstrate the correctness of this conclusion by comparison.展开更多
In this paper,we investigate the influence of the nonlocal prey competition on the spatiotemporal dynamics for a generalist predator-prey system.The condition of stability and bifurcations is clearly determined.Our re...In this paper,we investigate the influence of the nonlocal prey competition on the spatiotemporal dynamics for a generalist predator-prey system.The condition of stability and bifurcations is clearly determined.Our results show that when the prey spreads quickly,the nonlocal intraspecific competition of the prey does not affect the dynamics,however,when the prey spreads slowly,it can affect the dynamics.Besides,no Hopf bifurcation occurs if the ratio of the growth rate of the predator to prey is larger,otherwise,system has Hopf bifurcation and Hopf Bogdanov-Takens bifurcation and so on.It is surprised that the system only with the nonlocal prey competition has more rich dynamics than the system with the nonlocal competitions in both the prey and the predator.The coexistence of bistable spatially inhomogeneous steady states is also found.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2572022DJ05)Postdoctoral Program of Heilongjiang Province(No.LBHQ21060).
文摘In this paper,we study the effects of the nonlocal competition and double Allee effect in prey on a diffusive predator–prey model.We investigate the local stability of coexistence equilibrium in the predator–prey model by analyzing the eigenvalue spectrum.We study the consequence of double Allee effect on the prey population.Also,we discuss the existence of Hopf bifurcation under different parameters by using the gestation time delay of predators as a bifurcation parameter and analyzing the distribution of eigenvalues.By utilizing the normal form method and center manifold theorem,we have given some conditions that could determine the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions.Through our research,we obtain that the double Allee effect can affect the coexistence of prey and predator and induce periodic oscillations of the densities of prey and predator.In addition,the nonlocal competition can also affect the stability and homogeneity of the solutions,but may receive the consequences of the Allee effect as well as time delay.In the numerical simulation part,we further demonstrate the correctness of this conclusion by comparison.
基金supported by grants from the National Natural Science Foundation of China(Nos.11971143 and 12071105)the Natural Science Foundation of Zhejiang Province(No.LZ23A010001).
文摘In this paper,we investigate the influence of the nonlocal prey competition on the spatiotemporal dynamics for a generalist predator-prey system.The condition of stability and bifurcations is clearly determined.Our results show that when the prey spreads quickly,the nonlocal intraspecific competition of the prey does not affect the dynamics,however,when the prey spreads slowly,it can affect the dynamics.Besides,no Hopf bifurcation occurs if the ratio of the growth rate of the predator to prey is larger,otherwise,system has Hopf bifurcation and Hopf Bogdanov-Takens bifurcation and so on.It is surprised that the system only with the nonlocal prey competition has more rich dynamics than the system with the nonlocal competitions in both the prey and the predator.The coexistence of bistable spatially inhomogeneous steady states is also found.
