In this paper, a discrete-time prey-predator model with Allee effect is considered. The dynamical behavior of the model is investigated. The existence and stability conditions of the coexistence fixed point of the model are analyzed. By using bifurcation theory, it is shown that the model undergoes flip bifurcation. Also, numerical simulations are presented to support the obtained theoretical results. 39A33, 37G35, 39A30.
In this work, we present a delay general nonlinear discrete-time population model with and without Allee effects which occur at low population density. We investigated local stability conditions of equilibrium point of both models and we compared the local stability of the same equilibrium point of these two models. Obtained all theoretical results were supported by numerical simulations.
In this paper, a discrete predator-prey model with Allee effect which is obtained by the forward Euler method has been investigated. The local stability conditions of the model at the fixed point have been discussed. In addition, it is shown that the model undergoes Neimark-Sacker bifurcation by using bifurcation theory. Then, the direction of Neimark-Sacker bifurcation has been given. The OGY method is applied in order to control chaos in considered model due to emergence of Neimark-Sacker bifurcation. Some numerical simulations such as phase portraits and bifurcation figures have been presented to support the theoretical results. Also, the chaotic features are justified numerically by computing Lyapunov exponents. Because of consistency with the biological facts, the parameter values have been taken from literature [Controlling chaos and Neimark-Sacker bifurcation discrete-time predator-prey system, Hacet.
This article is about the dynamics of a discrete-time prey-predator system with Allee effect and immigration parameter on prey population. Particularly, we study existence and local asymptotic stability of the uniq ue positive fixed point. Furthermore, the conditions for the existence of bifurcation in the system are derived. In addition, it is shown that the system goes through period-doubling bifurcation by using bifurcation theory and center manifold theorem. Eventually, numerical examples are given to illustrate theoretical results.
Abstract:The growth of the populations depending on interspecific interactions may exhibit drastic changes. The stability of populations change not only interspecific interactions but also under external effects such as immigration effect. Thus, population models can show complex dynamics. Immigration effect often simplify the population dynamics; and tends to supress chaotic behavior. This situation which can allow the local stability analysis of population is important for control of a two species interacting system. In this paper, we investigated dynamics of a host-parasite model with the immigration parameter added to the host population under the constant searching efficiency. We conclude that immigration parameter produces certain interesting results.
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