On stability of discrete-time predator-prey systems subject to Allee effects
نویسندگان
چکیده
The stability of predator-prey system subject to the Allee effect is of considerable interest in recent times. The present investigation is an attempt to observe the stability nature of a discrete-time predator-prey system with Allee effect on predator, prey and on both the population. We have obtained the conditions for which the equilibrium points of each of the three cases are asymptotically stable. By mathematical analysis, phase plane and bifurcation analysis it is observed that, predation driven Allee on prey population has destabilizing effect on the model system and a wide range of dynamical behavior is observed from stable equilibrium points to unstable one through a regime of neutrally stable limit cycles. On the contrary, when Allee effect is present in predator only or both, the stability of the model system increases.
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