Yishu Wang’s research while affiliated with Nanjing Institute of Industry Technology and other places

In this article, we investigate globally exponential synchronization problems in delayed complex dynamic networks (DCDNs) characterized by both time‐varying impulsive delay and gain (TIDG). Our research is grounded on the Halanay inequality, which serves as the keystone of our analysis. Adopting the method of average impulsive delay‐gain (AIDG), we formulate criteria for globally exponential synchronization dependent on the overall impulsive disturbances. Our criteria reveal the negative effect of AIDG on synchronization, which hinders the synchronization process. Additionally, we refine the concept of average impulsive gain to enhance its applicability. Furthermore, our results demonstrate that even in the simultaneous presence of desynchronizing and synchronizing impulses, along with time‐varying impulsive delays, DCDNs are able to maintain the original synchronization under appropriate conditions, irrespective of whether the average impulsive interval is finite or not. Finally, we validate our theoretical findings by applying them to network examples.

This article explores the criteria for fixed‐time stability (FxTS) within nonlinear impulsive dynamical systems, encompassing both stabilizing and destabilizing impulses. Initially, employing the Lyapunov method, the article delineates a criterion for FxTS, particularly when impulsive sequences are delineated by an average impulsive interval. Following this, the article innovatively applies two integral inequalities to introduce an optimized criterion for uniform impulsive sequences, evidencing its lesser conservativeness relative to the initial criterion. Moreover, this article derives a necessary condition for dynamical systems subjected to destabilizing impulses. Intriguingly, the investigation reveals the existence of a minimal threshold for the maximum impulsive interval, below which the system cannot achieve FxTS. This result elucidates why existing literature uniformly imposes a specific condition on the impulsive interval for destabilizing impulses. Finally, the efficacy of the proposed theory is underscored through numerical examples.

This paper examines fixed-time synchronization (FxTS) for two-dimensional coupled reaction–diffusion complex networks (CRDCNs) with impulses and delay. Utilizing the Lyapunov method, a FxTS criterion is established for impulsive delayed CRDCNs. Herein, impulses encompass both synchronizing and desynchronizing variants. Subsequently, by employing a Lyapunov–Krasovskii functional, two FxTS boundary controllers are formulated for CRDCNs with Neumann and mixed boundary condition, respectively. It is observed that vanishing Dirichlet boundary contributes to the synchronization of the CRDCNs. Furthermore, this study calculates the optimal constant for the Poincaré inequality in the square domain, which is instrumental in analyzing FxTS conditions for boundary controllers. Conclusive numerical examples underscore the efficacy of the proposed theoretical findings.

This work focuses on exponential synchronization for a class of partially coupled heterogeneous networks with time-delays and heterogeneous impulses. The synchronization targets are selected as the common equilibrium solution and the average trajectory, respectively. Some synchronization criteria are deduced by using Lyapunov function and comparison principle.