Permanence and existence of periodic solution of a discrete periodic Lotka–Volterra competition system with feedback control and time delays

In this paper, we consider a discrete predator–prey system with feedback and time delays. By applying the theory of difference inequality, as well as analysis technique, sufficient conditions are obtained for the permanence of the system. And by applying Mawhin's coincidence degree theory, we obtain the existence of the positive periodic solutions

Beverton-Holt equation

Republic (in press)]. We extend their result and obtain a sufficient condition for attenuation of cycles in population models. This sufficient condition is applicable to a wide class of periodic difference equations with arbitrary period. For an illustration, the result is applied to the Beverton-Holt equation and other specific population models

Permanence of a Discrete Periodic Volterra Model with Mutual Interference

This paper discusses a discrete periodic Volterra model with mutual interference and Holling II type functional response. Firstly, sufficient conditions are obtained for the permanence of the system. After that, we give an example to show the feasibility of our main results

Feedback Control Variables Have No Influence on the Permanence of a Discrete n

We consider a discrete n-species Schoener competition system with time delays and feedback controls. By using difference inequality theory, a set of conditions which guarantee the permanence of system is obtained. The results indicate that feedback control variables have no influence on the persistent property of the system. Numerical simulations show the feasibility of our results

Permanence and Global Attractivity of a Delayed Discrete Predator-Prey System with General Holling-Type Functional Response and Feedback Controls

This paper discusses a delayed discrete predator-prey system with general Holling-type functional response and feedback controls. Firstly, sufficient conditions are obtained for the permanence of the system. After that, under some additional conditions, we show that the periodic solution of the system is global stable