This paper investigates the bipartite synchronization of stochastic coupled systems with hybrid time-varying delays and Markov jump via asynchronous impulsive control. Unlike existing studies, the asynchronous impulses considered in this paper are decentralized, which allows for the investigation of a wider range of dynamic properties. Additionally, to address asynchronous impulsive control, asynchronous average dwell-time condition is introduced for the first time, and new auxiliary functions are defined. Several sufficient criteria for attaining bipartite synchronization are derived through the application of the Lyapunov method and graph theory. In addition, the theoretical findings are applied to single-link robot arms with hybrid time-varying delays. To demonstrate the practicality of the findings, this paper includes two numerical examples.

This paper focuses on partial identification problems of coupled matrices for stochastic hybrid multi-layer delayed networks with inter-layer and intra-layer couplings and Markovian switching. The main approach is to combine Lyapunov method, Kirchhoff’s matrix-tree theorem and stochastic analysis. By pinning control technique, partial identification criterion is got. As a special case, the whole identification criterion is also derived. At last, three numerical examples of classical Lü and Lorenz systems are provided to demonstrate the validity of the presented results. Especially the impact of Markovian switching on partial topology identification is discussed. Note to Practitioners—This paper was motivated by existing results on synchronization of multi-layer complex network with stochastic perturbation. The existing results mainly focus on exponential synchronization or asymptotic synchronization based on known coupled matrices of networks. In this paper, the coupled matrices are unknown, the drive-response systems can achieve the partial synchronization with probability one via pinning controller. Furthermore, combining with stochastic version of the LaSalle theorem, the partial identification of coupled matrices criterion has been obtained. It should be noted that the Markovian switching and time delay in this work play an important role in the identification.

This paper investigates the stabilization of highly nonlinear stochastic delayed large-scale networks (HSDLN) based on asynchronously delayed intermittent decentralized control (ADIDC). By incorporating highly nonlinearity into the networks, practical problems can be more accurately modeled, and the nonlinear coupling relationships among nodes can be effectively captured, vastly expanding the practical application scope. ADIDC effectively integrates the advantages of asynchronously intermittent decentralized control and delayed intermittent control, enabling the networks to achieve the desired behavior. Subsequently, we set up an auxiliary timer and then define a newfangled Lyapunov functional. In particular, an innovative Lyapunov-based analysis, not utilizing Halanay-type differential inequality, is introduced to obtain a stabilization criterion for HSDLN, which effectively copes with asynchronously intermittent decentralized control and highly nonlinear, stochastic, and delayed elements. Meanwhile, a graph-theoretic methodology is employed to address the cross-terms arising in an asynchronous sense. Ultimately, as a practical application of the theoretical findings, a class of FitzHugh-Nagumo models is considered, and the stabilization is validated through numerical simulations. Note to Practitioners—This paper is motivated by existing results on various intermittent controls for the dynamics of complex networks. The existing results mainly require intermittent controls to be continuously/discretely synchronous sampled-data each node of complex networks, which limits the application scope of intermittent controls. This paper designs a new hybrid control called asynchronously delayed intermittent decentralized control. Particularly, asynchronously intermittent sampled-data control is a special case of control in this paper. Moreover, some lower conservative sufficient conditions are derived, such as local Lipschitz condition and polynomial growth condition instead of global Lipschitz condition and linear growth condition for coefficients of complex networks, and the average work time ratio instead of the maximum rest time ratio for intermittent control. The proposed results provide a novel idea for the stabilization study of FitzHugh-Nagumo models, and it is expected that the proposed methods can be extended to more actual physical engineering systems.

This article focuses on stabilizing highly nonlinear hybrid stochastic complex dynamical networks with time delays (HSCNT) via sampled-data control with asynchronously periodic self-triggered intermittent decentralized strategy (SCAPI). Considering the constraints imposed by linear growth conditions in real models, we introduce high nonlinearity into the networks. Moreover, considering the possibility of nonsimultaneous transmission of control information by the controllers, the asynchronous decentralization is thus brought in periodic self-triggered intermittent control for the first instance. Then, to resolve the problems caused by asynchronous decentralization, a graph-theoretic approach is employed. Combining this with an auxiliary timer, an innovative Lyapunov functional is designed, after which an original Lyapunov-based method is proposed to cope with the complexity of introducing high nonlinearity and asynchronous decentralization into networks. In particular, some numerical simulations are provided for demonstration.

In the article, a stabilized issue for complex-valued hybrid stochastic multilinks networks (CHSMNs) is investigated under event-triggered control (E-TC). In contrast to existing literature, the proposed E-TC defines the event-triggered instant sequence as the random sequence rather than the number sequence, which is more accurate concerning hybrid stochastic systems. Especially, a modified more general event-triggered function is proposed. After the Zeno behavior is eliminated by the contradiction, several stabilized conditions are established to guarantee the input-to-state stability and exponential stability in the mean square and almost surely exponential stability of CHSMNs, where studying in the complex domain and no splitting real and imaginary parts. Subsequently, we analyze the lower bound of the event-triggered intervals for E-TC in the sense of mathematical expectation. Whereafter, the stabilized problem for the Cohen–Grossberg neural networks (CSDLCNs) and the islanded micro grid model (IMGM) is considered as an application. Meanwhile, numerical simulations are presented for verification.