On the Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks

AbstractA set of criteria is presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov functionals, introducing many parameters and combining with the elementary inequality technique. These criteria have important leading significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, earlier results are extended and improved; other results are contained. Two examples are given to illustrate the theory

Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results

Gossip Consensus Algorithm Based on Time-Varying Influence Factors and Weakly Connected Graph for Opinion Evolution in Social Networks

We provide a new gossip algorithm to investigate the problem of opinion consensus with the time-varying influence factors and weakly connected graph among multiple agents. What is more, we discuss not only the effect of the time-varying factors and the randomized topological structure but also the spread of misinformation and communication constrains described by probabilistic quantized communication in the social network. Under the underlying weakly connected graph, we first denote that all opinion states converge to a stochastic consensus almost surely; that is, our algorithm indeed achieves the consensus with probability one. Furthermore, our results show that the mean of all the opinion states converges to the average of the initial states when time-varying influence factors satisfy some conditions. Finally, we give a result about the square mean error between the dynamic opinion states and the benchmark without quantized communication

How to empower Grünwald–Letnikov fractional difference equations with available initial condition?

In this paper, the initial condition independence property of Grünwald–Letnikov fractional difference is revealed for the first time. For example, the solution x(k) of equation aG∇kαx(k) = f(x(k)),  k > a + 1, cannot be calculated with initial condition x(a). First, the initial condition independence property is carefully investigated in both time domain and frequency domain. Afterwards, some possible schemes are formulated to make the considered system connect to initial condition. Armed with this information, the concerned property is examined on three modified Grünwald–Letnikov definitions. Finally, results from illustrative examples demonstrate that the developed schemes are sharp

Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term

This paper is concerned with the stability problem for a class of uncertain impulsive stochastic genetic regulatory networks (UISGRNs) with time-varying delays both in the leakage term and in the regulator function. By constructing a suitable Lyapunov-Krasovskii functional which uses the information on the lower bound of the delay sufficiently, a delay-dependent stability criterion is derived for the proposed UISGRNs model by using the free-weighting matrices method and convex combination technique. The conditions obtained here are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI control toolbox. In addition, three numerical examples are given to justify the obtained stability results

Leader-following identical consensus for Markov jump nonlinear multi-agent systems subjected to attacks with impulse

The issue of leader-following identical consensus for nonlinear Markov jump multiagent systems (NMJMASs) under deception attacks (DAs) or denial-of-service (DoS) attacks is investigated in this paper. The Bernoulli random variable is introduced to describe whether the controller is injected with false data, that is, whether the systems are subjected to DAs. A connectivity recovery mechanism is constructed to maintain the connection among multi-agents when the systems are subjected to DoS attack. The impulsive control strategy is adopted to ensure that the systems can normally work under DAs or DoS attacks. Based on graph theory, Lyapunov stability theory, and impulsive theory, using the Lyapunov direct method and stochastic analysis method, the sufficient conditions of identical consensus for Markov jump multi-agent systems (MJMASs) under DAs or DoS are obtained, respectively. Finally, the correctness of the results and the effectiveness of the method are verified by two numerical examples