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Stability and Hopf bifurcation in a class of ecological system with time delay. (Chinese. English summary) Zbl 1174.34515
Summary: The properties of the solutions in a predator-prey system with finite delay are studied. Using the time lag $$\tau$$ as a parameter, the stability and Hopf bifurcation of the equilibriums in a predator-prey system are analyzed. The results obtained are sufficient conditions for stability and the occurrence of Hopf bifurcation.
MSC:
 34K60 Qualitative investigation and simulation of models involving functional-differential equations 34K18 Bifurcation theory of functional-differential equations 34K20 Stability theory of functional-differential equations 92D40 Ecology