Abstract
A class of predator-prey system with distributed delays and competition term is considered. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the predator-prey system. According to the theorem of Hopf bifurcation, some sufficient conditions are obtained for the local stability of the positive equilibrium point.
Highlights
Delay differential equations display more complicated dynamics than ordinary differential equations as a time delay could bring a switch in the stability of equilibria and induce various oscillations and periodic solutions
Neural Networks with time delay or distributed delays have been investigated by some researchers [1,2,3,4]
Time delay has a strong impact on the dynamic evolution of a population, which could bring a switch in the stability of equilibria and induce various oscillations and periodic solutions
Summary
Delay differential equations display more complicated dynamics than ordinary differential equations as a time delay could bring a switch in the stability of equilibria and induce various oscillations and periodic solutions. A class of predator-prey system with distributed delays and competition term is considered. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the predator-prey system.
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