This paper investigates the finite-time bipartite synchronization (FTBS) problem in multilayer signed networks subject to semi-Markovian switching topologies and stochastic disturbances. A comprehensive framework is developed that simultaneously incorporates: (i) multilayer network with antagonistic interactions, (ii) semi-Markovian jump parameters, and (iii) stochastic noise effects, addressing key challenges in modeling heterogeneous, nonlinearly coupled systems operating in random environments. For the first time, FTBS is achieved through aperiodically intermittent control strategies. By combining graph-theoretic analysis with Lyapunov stability theory, some sufficient conditions for ensuring FTBS are established under the proposed control scheme. The theoretical results are rigorously verified through numerical simulations, demonstrating their feasibility and effectiveness.

This paper concentrates on the almost sure synchronization for a class of stochastic multi-links coupled semi-Markov jump systems through aperiodically intermittent control. For these stochastic switching systems, almost sure synchronization is investigated by employing mode-dependent multiple Lyapunov-like function method and stochastic analysis. Notably, mode-dependent multiple Lyapunov-like function method is designed to provide more flexibility. In addition, when considering the sojourn time distribution of the semi-Markov jump, dependence on both the current state and the next state can effectively reduce unnecessary restrictions compared with previous assumption of the sojourn time distribution function. Ultimately, the Chua’s circuit along with numerical simulations are provided to validate the effectiveness of the theoretical results.

This paper investigates the pth moment exponential synchronization problem of multi-links stochastic delayed complex networks with semi-Markov jump via aperiodically intermittent control. Combining random disturbances, time-varying delay and semi-Markov jump with multi-links systems, our work is more relevant than previous work. Based on Lyapunov method and graph theory, a novel inequality for disposing of the problem of pth exponential synchronization is established under the aperiodically intermittent control and some sufficient criteria are derived. The theoretical results supply a new perspective showing the synchronization criterion and the topological structure of multi-links systems related closely. Furthermore, the value of our results is exhibited by applying them to the single-link robot arms in engineering. Eventually, a numerical simulation is provided to demonstrate the validity of our results.

In this paper, we investigate the exponential synchronization problem for multi-link and multi-delayed inertial neural networks with Markov jump (MMDINNMJ) using an aperiodically intermittent adaptive control strategy. Different from most research on inertial neural networks, we take multi-link, multi-delay and Markov jump into account. The obstacle caused by the coexistence of Markov jump and multi-delay is avoided by using the delayed integral method while considering the exponential synchronization of MMDINNMJ. Additionally, under graph theory, Lyapunov stability theory and the developed control scheme, some novel sufficient conditions for synchronization at exponential rate in pth (p>0) moment of underlying networks are determined, which are strongly related to multi-link topological structure, time delay, and Markov jump. Finally, two examples are given to demonstrate the viability of the theoretical conclusions.

In this paper, we investigate the issue of almost sure stability (ASS) for a class of stochastic strict-feedback semi-Markov jump systems (SSSJSs) under periodic intermittent control (PIC). This control method and dynamic properties are studied for the first time in strict-feedback systems. First of all, based on the structural properties of the SSSJSs, virtual controllers are designed step by step and eventually deduced into the actual controller. Furthermore, by using stochastic analysis theory and multiple Lyapunov function method, we obtain sufficient conditions for ASS via PIC, which have a close relationship with control width and control period. By virtue of multiple Lyapunov functions that depend on the system states, the conservatism caused by mode-independent cases can be reduced effectively. Finally, the effectiveness of the presented results is illustrated by simulation examples.

This paper focuses on exponential synchronization for multi-link and multi-delayed large-scale systems with semi-Markov jump (MLMDLSSMJ) via adaptive aperiodically intermittent control. It is challenging to overcome the impacts of multiple time delays and semi-Markov jump because of the intermittent property. The multi-delayed differential inequalities with semi-Markov jump are established to address this issue, which extend the existing Halanay-type differential inequalities. Several exponential synchronization criteria for intermittently controlled MLMDLSSMJ are built by using the inequality technique, Lyapunov method and graph theory. Notably, the exponential convergence rate is more accurate than the previous literature, which may aptly show the synchronization capability of MLMDLSSMJ. The exponential synchronization of Chua’s circuits network is investigated as a practical implementation of the theoretical results. Finally, to demonstrate the efficiency of the theoretical results, a few numerical simulations are provided.

In this paper, the issue of exponential synchronization in Markov switching inertial neural networks with mixed delays is investigated via aperiodically on–off adaptive control. The inertial term is considered, which extends the existing network modes with first-order differential term. Combined with the Lyapunov method, graph theory, and the differential inequalities technique, two types of synchronization criteria are presented which take into account all of the time delay information and reduce the conservativeness. Finally, some numerical simulations are provided in order to show the validity of the theoretical results.

In this paper, exponential synchronization for hybrid multi‐weighted complex networks is studied via aperiodically intermittent control. Different from previous work, both Markov jump and reaction‐diffusion effects are simultaneously considered into multi‐weighted complex networks. By employing network split technique, graph theory, and Lyapunov method, several synchronization criteria are derived. These criteria show the effects of multiple weights, Markov jump, and reaction‐diffusion on exponential synchronization. Furthermore, an application to Cohen–Grossberg neural networks is conducted, and the corresponding synchronization criterion is given. Finally, some numerical simulations are presented to show the effectiveness of the obtained theoretical results.

In this paper, the problem of exponential synchronization is studied for a class of stochastic coupled networks with semi-Markovian jump and multiple time delays. A nonlinear aperiodical intermittent control is designed to synchronize the underlying networks. By Lyapunov approach and graph theory, some new synchronization criteria are derived, which are closely related to the maximum uncontrolled ratio of intermittent control and the network topology structure. Synchronization analysis for coupled oscillators is conducted to show the practical potential of the obtained theoretic results. Also, two numerical examples are given to illustrate the effectiveness of control strategy.

This paper investigates the problem of inner exponential synchronization (IES) for delayed coupled systems on networks (DCSNs) via periodically intermittent control. Both internal time-varying delay and coupling time-varying delay are all taken into account. By combining graph theory with Lyapunov method, some sufficient criteria are derived to ensure DCSNs under periodically intermittent control can be inner exponentially synchronized. Furthermore, IES of delayed coupled oscillators on a network is studied to verify the theoretical results. Finally, a numerical example is provided to illustrate the feasibility of our analytical results.

In this paper,pth-moment exponential synchronization for Markovian jump stochastic complex networks with time-varying delays (MJSCNTVDs) is studied via aperiodically intermittent control. By combining graph theory andM-matrix theory, some novel synchronization criteria are derived, which comprise two forms: (1) Lyapunov-type criteria and (2) coefficient-type criteria. As its applications, the obtained synchronization results are applied to explorepth-moment exponential synchronization of stochastic coupled oscillators with time-varying delays and Markovian jump. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required and that the restriction between control width and delay is removed. Two numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained.

This paper is concerned with exponential synchronization of semi-Markov jump complex networks via adaptive aperiodically intermittent control. Time-varying delay, stochastic perturbation, semi-Markov jump topology are all taken into consideration to make model more general. It should be pointed that, a semi-Markov jump adaptive aperiodically intermittent controller is designed as well. The synchronization analysis is carried out based on the combination of Lyapunov method and graph theory. Moreover, some novel synchronization criteria are established, which are closely related to the maximum uncontrolled ratio and the topological structure of considered networks. Furthermore, the obtained results are applied to stochastic coupled oscillators, and the corresponding numerical simulations are provided to illustrate the applicability and effectiveness of the proposed control strategy.

In this paper, the exponential stability of delayed coupled systems on networks (DCSNs) is investigated via periodically intermittent control. By utilizing graph-theoretic approach and Lyapunov function method, a novel method for stability analysis of DCSNs is developed. Moreover, some useful and easily verifiable sufficient conditions are presented in the form of Lyapunov-type theorem and coefficients-type criterion. These laws reveal that the stability has a close relationship with the topology structure of the networks. In addition, as a subsequent result, the obtained theory is successfully applied to study the exponential stability of delayed coupled oscillators on networks under periodically intermittent control. Finally, a numerical example is given to validate the effectiveness of theoretical results.

In this paper, the issue of exponential synchronization for coupled systems on networks with mixed time-varying delays is concerned. An approach combining Kirchhoff’s matrix tree theorem in graph theory with Lyapunov method and periodically intermittent control is taken to investigate the problem. This method is different from the corresponding previous works. Two different kinds of synchronization conditions in the form of Lyapunov-type theorem and coefficients-type criterion are derived. They both reveal synchronization has a close relation with the topology structure of the network. Finally, the feasibility and effectiveness of the proposed method are illustrated by several numerical simulation figures.

The nonlinear fractional-order Fokker–Planck differential equations have been used in many physical transport problems which take place under the influence of an external force filed. Therefore, high-accuracy numerical solutions are always needed. In this article, reproducing kernel theory is used to solve a class of nonlinear fractional Fokker–Planck differential equations. The main characteristic of this approach is that it induces a simple algorithm to get the approximate solution of the equation. At the same time, an effective method for obtaining the approximate solution is established. In addition, some numerical examples are given to demonstrate that our method has lesser computational work and higher precision.

This paper mainly focus on the exponential stabilization problem of coupled systems on networks with mixed time‐varying delays. Periodically intermittent control is used to control the coupled systems on networks with mixed time‐varying delays. Moreover, based on the graph theory and Lyapunov method, two different kinds of stabilization criteria are derived, which are in the form of Lyapunov‐type theorem and coefficients‐type criterion, respectively. These laws reveal that the stability has a close relationship with the topology structure of the networks. In addition, as a subsequent result, a decision theorem is also presented. It is straightforward to show the stability of original system can be determined by that of modified system with added absolute value into the coupling weighted‐value matrix. Finally, the feasibility and validity of the obtained results are demonstrated by several numerical simulation figures.

The novelty and innovativeness of this paper are the combination of reproducing kernel theory and spline, this leads to a new simple but effective numerical method for solving variable-order anomalous sub-diffusion equation successfully. This combination overcomes the weaknesses of piecewise polynomials that can not be used to solve differential equations directly because of lack of the smoothness. Moreover, new bases of reproducing kernel spaces are constructed. On the other hand, the existence of any ε-approximate solution is proved and an effective method for obtaining the ε-approximate solution is established. A numerical example is given to show the accuracy and effectiveness of theoretical results.