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Hopf bifurcation and stability analysis in a harvested one-predator-two-prey model. (English) Zbl 1017.92041
Summary: Hopf bifurcation is demonstrated in an interacting one-predator-two-prey model with harvesting of the predator at a constant rate. Here the harvest rate is used as a control parameter. It is found that periodic solutions arise from stable stationary states when the harvest rate exceeds a certain limit. The stability of these periodic solutions is investigated with the variation of this control parameter. The approach is analytic in nature and the normal form analysis of the model is performed.
MSC:
92D40Ecology
34C23Bifurcation (ODE)
34C60Qualitative investigation and simulation of models (ODE)
93C95Applications of control theory