The stable switching phenomenon of a diffusion mussel-algae system with two delays and half saturation constant is studied.The stability of positive equilibrium and the existence of Hopf bifurcation on two-delay plane...The stable switching phenomenon of a diffusion mussel-algae system with two delays and half saturation constant is studied.The stability of positive equilibrium and the existence of Hopf bifurcation on two-delay plane are investigated by calculating the stability switching curves.The normal form on the central manifold near Hopf bifurcation point is also derived.It can find that two different delays can induce the stable switches which cannot occur with the same delays.Through numerical simulations,the region of complete stability of system increases with the increase of half-saturation constant,indicating that the half-saturation constant contributes to the stability of system.In addition,double Hopf bifurcations may occur due to the intersection of bifurcation curves.These results show that two different delay and half-saturation constant have important effects on the system.The numerical simulation results validate the correctness of the theoretical analyses.展开更多
基金supported by Hebei Natural Science Foundation(A2024409003).
文摘The stable switching phenomenon of a diffusion mussel-algae system with two delays and half saturation constant is studied.The stability of positive equilibrium and the existence of Hopf bifurcation on two-delay plane are investigated by calculating the stability switching curves.The normal form on the central manifold near Hopf bifurcation point is also derived.It can find that two different delays can induce the stable switches which cannot occur with the same delays.Through numerical simulations,the region of complete stability of system increases with the increase of half-saturation constant,indicating that the half-saturation constant contributes to the stability of system.In addition,double Hopf bifurcations may occur due to the intersection of bifurcation curves.These results show that two different delay and half-saturation constant have important effects on the system.The numerical simulation results validate the correctness of the theoretical analyses.
