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Ratio dependent predation: A bifurcation analysis. (English) Zbl 0913.92028

Summary: We have considered a prey-predator model reflecting the predator interference with discrete time delay. This delay is regarded as the lag due to gestation. In absence of delay, criteria for existence of an interior equilibrium and its global stability are derived. By choosing the delay as a bifurcation parameter, we have shown that a Hopf bifurcation may occur when the delay passes its critical value. Finally, we have derived the criteria for stability switches and verified the results through computer simulation.

MSC:

92D40 Ecology
34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
34K18 Bifurcation theory of functional-differential equations
34C23 Bifurcation theory for ordinary differential equations
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