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

Dynamic behaviors of a delay differential equation model of plankton allelopathy

AbstractIn this paper, we consider a modified delay differential equation model of the growth of n-species of plankton having competitive and allelopathic effects on each other. We first obtain the sufficient conditions which guarantee the permanence of the system. As a corollary, for periodic case, we obtain a set of delay-dependent condition which ensures the existence of at least one positive periodic solution of the system. After that, by means of a suitable Lyapunov functional, sufficient conditions are derived for the global attractivity of the system. For the two-dimensional case, under some suitable assumptions, we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation. Examples show the feasibility of the main results

The Complex Dynamics of a Stochastic Predator-Prey Model

A modified stochastic ratio-dependent Leslie-Gower predator-prey model is formulated and analyzed. For the deterministic model, we focus on the existence of equilibria, local, and global stability; for the stochastic model, by applying Itô formula and constructing Lyapunov functions, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. Based on these results, we perform a series of numerical simulations and make a comparative analysis of the stability of the model system within deterministic and stochastic environments