Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin–Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

On the Oscillation of Conformable Impulsive Vector Partial Differential Equations

In this paper, we study the oscillations of a class of conformable impulsive vector partial functional differential equations. For this class, our approach is to reduce the multi-dimensional oscillation problems to that of one dimensional impulsive delay differential inequalities by applying inner product reducing dimension method and an impulsive differential inequality technique. We provide an example to illustrate the effectiveness of our main results.

Synchronization Analysis of Complex Dynamical Networks Subject to Delayed Impulsive Disturbances

This paper studies the problem of leader-following synchronization for complex networks subject to delayed impulsive disturbances, where two kinds of time delays considered exist in internal complex networks and impulsive disturbances. Some delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs) by using the delayed impulsive differential inequality method. Moreover, a feedback controller is designed to realize desired synchronization via the established LMIs. Our proposed results show that the requirements of impulse intervals and impulse sizes are dropped, and delayed impulses and large scale impulses are allowed to coexist. Finally, some examples are given to show the effectiveness of the obtained results.

Research on Computer Virus Prevention Strategies

In this paper, an model with impulsive effect is considered. The existence of the periodic virus-free solution is given and the basic reproductive number is defined. Using the Floquet theory and impulsive differential inequality, we obtain the local and global stability of the periodic virus-free solution if , and the virus in the computers will be eliminated. Finally numerical simulation validates the results and shows that the periodic virus-free solution is unstable and the virus will persist when .

Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous results. Finally, two numerical examples are given to illustrate the advantages of the obtained results.

Exponential Synchronization for Impulsive Dynamical Networks

This paper is devoted to exponential synchronization for complex dynamical networks with delay and impulsive effects. The coupling configuration matrix is assumed to be irreducible. By using impulsive differential inequality and the Kronecker product techniques, some criteria are obtained to guarantee the exponential synchronization for dynamical networks. We also extend the delay fractioning approach to the dynamical networks by constructing a Lyapunov-Krasovskii functional and comparing to a linear discrete system. Meanwhile, numerical examples are given to demonstrate the theoretical results.