In this paper,a delayed diffusive predator-prey model with fear effect under Neumann boundary conditions is considered.For the system without diffusion and delay,the conditions for the existence and local stability of...In this paper,a delayed diffusive predator-prey model with fear effect under Neumann boundary conditions is considered.For the system without diffusion and delay,the conditions for the existence and local stability of equilibria are obtained by analyzing the eigenvalues.Then,the instability induced by diffusion and delay-diffusion of the positive constant stationary solutions are discussed,respectively.Moreover,the regions of instability and pattern formation can be achieved with respect to diffusion and delay coefficients.Furthermore,the existence and direction of Hopf bifurcation and the properties of the homogeneous/nonhomogeneous bifurcated periodic solutions are driven by using the center manifold theorem and the normal form theory.Finally,some numerical simulations are carried out to verify the theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12171135 and 11771115)the Natural Science Foundation of Hebei Province(Nos.A2020201021 and A2019201396)+1 种基金the Post Doctor Start-up Foundation of Zhejiang Normal University(No.ZC304021906)the Research Funding for High-Level Innovative Talents of Hebei University(No.801260201242).
文摘In this paper,a delayed diffusive predator-prey model with fear effect under Neumann boundary conditions is considered.For the system without diffusion and delay,the conditions for the existence and local stability of equilibria are obtained by analyzing the eigenvalues.Then,the instability induced by diffusion and delay-diffusion of the positive constant stationary solutions are discussed,respectively.Moreover,the regions of instability and pattern formation can be achieved with respect to diffusion and delay coefficients.Furthermore,the existence and direction of Hopf bifurcation and the properties of the homogeneous/nonhomogeneous bifurcated periodic solutions are driven by using the center manifold theorem and the normal form theory.Finally,some numerical simulations are carried out to verify the theoretical results.
