Hopf Bifurcation Analysis of Predator-Prey System with Time Delay and Harvest Terms
For a class of predator-prey system with Leslie-Gower functional response function,the global stability of the equilibrium point of the system is analyzed by using the delays τ1,τ2 bifurcation parameter comparison theory,and the local stability of the posi-tive equilibrium point of the system,the conditions and branching direction of Hopf branching at the positive equilibrium point are analyzed by using the gauge theory and the judgment of the positive and negative real parts of the characteristic root.Finally,ac-cording to the global branching theory,the stability conclusion of local Hopf bifurcation is extended to the whole,and the correct-ness of the conclusion is verified by numerical simulation.
time delaysLeslie-Gower predator-prey systemHopf bifurcationstabilityperiodic solutions
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