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Hopf Bifurcation in the Third-Dimensional Ecologic Dynamical System

Wu yunhua; Yuan xiaofeng; Liu shize(Ceder for Mathematical Sciences Chengdu Institute of Computer Application, Academia Sinica 610041 )  
A class of ecology models in predator-prey systems is considered. The bifurcationphenomena are discussed by using Hopf bifurcation and Center manifold theorems. Hopf bifurcation can occur in some values of parameters. The asymptotic formulas fot the center manifoldand the periodic solution with small amplitude have been given. The stable criterion of the periodic solution has also been obtained.
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