Bifurcation and Stability of Prey-Predator Model with Beddington-DeAngelis Functional Response

In this paper we discuss the harvesting of the prey species making a fraction of them to be accessed by the predator while both the prey and predator are being subjected to Beddington-DeAngelis functional response. It is observed that a Hopf-bifurcation may occur around the interior equilibrium taking the environmental carrying capacity of the prey species as the parameter. Some numerical examples and the corresponding curves are studied using Maple to explain the results of the proposed model

Periodic Solutions Generated by Impulses for State-Dependent Impulsive Differential Equation

We study the existence of periodic solutions for a class of state-dependent impulsive differential systems via geometrical analysis methods. Our results show that these periodic solutions are generated by impulses. Moreover, numerical simulations are used to examine the existence of the periodic solutions

Behavior of the Solutions for Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on Periodic Time Scales in Shifts

We consider two-dimensional predator-prey system with Beddington-DeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system has δ±-periodic solution

Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control

A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results