Sufficient Conditions For Synchronization Research Articles

Quasi-projective synchronization of memristor-based complex valued recurrent neural network with time-varying delay and mismatched parameters

This article focuses on the quasi-projective synchronization for a class of non-identical memristor-based complex-valued recurrent neural networks (MCVRNNs) with time-varying delays and parameters’ mismatched. Here, the quasi-projective synchronization is presented in two ways based on the Halanay inequality and some useful techniques. Some novel sufficient conditions are firstly derived for quasi-projective synchronization criteria of non-identical memristor-based CVRNNs with time-varying delays and parameters’ mismatched by using the matrix measure method. And then, by using the Lyapunov-Krasovskii functional, another sufficient stabilization condition for quasi-projective synchronization of the concerned model is presented. Finally, two numerical simulation results are given to demonstrate the usefulness and persistence of the proposed methods under some conditions.

Inter-layer synchronization on a two-layer network of unified chaotic systems: The role of network nodal dynamics

The interplay between synchronization across layers and structures within layers still remains far unclear in multi-layer networks. Via our newly-constructed two-layer network consisting of the unified chaotic systems where the link within layer is linearly coupled and the link across layers is formed via sharing a common signal, this paper investigates the inter-layer synchronization on two-layer networks from the perspective of network nodal dynamics, as well as explore the influence of intra-layer network structures on inter-layer synchronization. Here we derive an analytical sufficient condition for inter-layer synchronization, which is only dependent on network nodal dynamics, showing a handful of Lorenz-type oscillators including the classic one are able to successfully realize inter-layer synchronization of the network for any connected intra-layer topological structures and diagonal coupling matrices. Further, four regular networks, small-world, scale-free and random networks are respectively used to run numerical simulations. Numerical results verify the presented theoretical results, and also show that Lü-type as well as Chen-type oscillators networks fail to realize inter-layer synchronization no matter which kinds of topologies and coupling matrices within layers. Specifically, for the case of identical topologies within layers, the chain-type and ring-type structures can stimulate larger range of Lorenz-type oscillators into synchronization across layers under the assumption of diagonal coupling matrices, but the fully-connected and star-type structures fail, and the non-diagonal intra-layer coupling matrix on the whole weaken the inter-layer synchronizability. For the case of nonidentical topologies within layers, the connection structure within layers can hardly enlarge the range of oscillators for synchronization across layers, even narrow the range, but some structures may enlarge the range of coupling strengthes for inter-layer synchronization.

Synchronization of switched complex dynamical networks with impulses: state-dependent switching approach

This paper studies the globally exponential synchronization (GES) of a class of complex dynamical networks (CDNs) with switching topology involving impulse action. A novel state-dependent switching (SDS) approach to tune the switching topology of CDNs is designed based on the information of the node dynamics with impulses. Different from the traditional SDS results which are based on continuous state space, some sufficient conditions for network synchronization based on SDS are proposed in the framework of impulse action. A relationship between impulse action, the network structure, and switching topology is established, which is crucial to design the SDS law. Two different impulse actions on the network dynamics are fully considered in this paper, namely, stabilizing continuous dynamics with desynchronizing impulses and destabilizing continuous dynamics with synchronizing impulses. Finally, two numerical simulations are given to demonstrate the effectiveness of the proposed control method.

Fixed/predefined-time synchronization of coupled memristor-based neural networks with stochastic disturbance

In this paper, with the design of a unified adaptive controller, the fixed-time (FXT) and predefined-time (PDT) synchronization problems of coupled memristor-based neural networks (CMNNs) with stochastic disturbance is studied. The FXT synchronization of CMNNs with stochastic disturbance via adaptive control is investigated, some sufficient conditions for FXT synchronization and a less conservative settling time independent of the initial state are given. By modifying the parameters of the same controller, the synchronization scheme of CMMNs within an arbitrary predefined time, which is not related to the system and controller parameters, is designed. Numerical simulations are finally given to verify the validity of the obtained theoretical results and the feasibility of the secure communication scheme.

Absolute Stability and Synchronization in Second-Order Neural Fields with Conduction Delays

We consider a class of neural field models represented by a second-order nonlinear system of integro-differential equations with space-dependent delays. Such a system models interaction of populations of neurons, each with a continuum description. We justify the existence and uniqueness of solution for the system in a suitable function space. Global existence and boundedness of solutions for the system are confirmed. Two methodologies, the comparison argument and sequential contracting, are developed to establish sufficient conditions for absolute stability and synchronization among different populations of the system. Finally, we present some numerical examples to demonstrate the theoretical results.

Exponential Bipartite Synchronization of Fractional-Order Multilayer Signed Networks via Hybrid Impulsive Control.

This article investigates the problem of exponential bipartite synchronization of fractional-order multilayer signed networks via hybrid impulsive control. First, the mathematical model of the networks is established by integrating the fractional dynamics of nodes, the multilayer network edges, and the positive and negative weights (antagonistic relationship), which is more pluralistic and practical. Second, a hybrid impulsive controller is designed, which is composed of the feedback control part and the impulsive control part to realize the exponential bipartite synchronization objective. Both positive and negative impulsive effects are considered and the ranges of the impulsive control gain related to the order of Caputo fractional derivative are discussed. In addition, some sufficient conditions for exponential bipartite synchronization of fractional-order multilayer signed networks are obtained by using the signed graph theory, Lyapunov method, and average impulsive interval method. Furthermore, in order to illustrate the practicability of the theoretical results, fractional-order coupled Chua's circuits model and fractional-order power systems built on multilayer signed networks are established and the exponential bipartite synchronization issues are analyzed. Numerical examples and simulations are provided to show the effectiveness of the obtained results.

Event-triggered synchronization of a two-layer heterogeneous neural network via hybrid control

Multi-layer network contains multiple subsystems and different types of interaction, which is more practical than traditional single-layer network. On this observation, this paper explores point-to-point quasi-synchronization in a two-layer heterogeneous neural network system. The sufficient conditions for global exponential synchronization in the driving layer are given a coupling term. Based on the global exponential synchronization in the driver layer, this paper further studies the global point-to-point quasi-synchronization between the driver layer and the response layer of the two-layer neural network under the hybrid control and event-triggered control. Under this hybrid control strategies, the event can be activated if and only if the trigger condition is violated and the dynamical adaptive control is also involved. Moreover, the Zeno behavior under this strategy is eliminated by Lyapunov method and matrix theory. Finally, a numerical example is given to verify the theoretical results.

Internet of health things encryption via master-slave synchronization for stochastic quaternion-valued neural networks

This paper investigates the problem of master-slave synchronization of stochastic quaternion-valued neural networks (SQVNNs) with mixed time-varying delays. A linear feedback controller is developed to explore the global synchronization of the proposed system by utilizing the complete information of the time-delay state. Sufficient conditions for synchronization of the proposed model are derived by constructing appropriate Lyapunov–Krasovskii functional by applying the master-slave synchronization method of master-slave and some integral inequality techniques. Finally, a corresponding numerical simulation is presented to demonstrate the accuracy of the theoretical results. This paper introduces a unique and efficient image encryption algorithm based on SQVNNs. This technique utilizes the solution set of SQVNNs to generate the high-level randomness secret keys to encrypt the source image. Finally, we conclude that the algorithm yields a source image cipher with excellent diffusion and confusion properties. A few test clinical images are utilized to show the validity of the proposed method. Several performance analyses show that the proposed algorithm for image encryption gives an efficient and secure way to deal with the Internet of Health Things (IoHT).

Event-triggered gain-scheduling dissipative synchronization control for switched neural networks under state-dependent switching

The dissipative synchronization problem of delayed Markov jump switched neural networks (MJSNNs) under state-dependent switching by the event-triggered gain-scheduling control scheme is studied in this paper. By the introduction of a Markov jump model, which is used to depict the random variation wherein the connection of MJSNNs, the issues we study can take more generality. Via constructing suitable Lyapunov–Krasovskii functionals (LKFs) and applying some matrix inequality scaling methods, sufficient conditions for dissipative synchronization of delayed MJSNN are established. According to such criteria, the event-triggered gain-scheduling control scheme is adopted to design a controller with less terminal communication costs. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Further results for synchronization of two coupled Boolean networks

AbstractThis paper investigates the complete synchronization of drive‐response Boolean networks (BNs) using the semi‐tensor product of matrices. First, a necessary and sufficient condition for complete synchronization is obtained. Next, a pinning control method for achieving complete synchronization of drive‐response BNs is proposed, based on certain transformations of the state transition matrix of drive BN. Then, an algorithm is proposed to obtain the minimum number of pinning nodes, based on the perturbation method. Finally, two numerical examples are given to verify the validity of the study results.

Cluster synchronization of coupled complex-valued neural networks with leakage and time-varying delays in finite-time

<abstract><p>In cluster synchronization (CS), the constituents (i.e., multiple agents) are grouped into a number of clusters in accordance with a function of nodes pertaining to a network structure. By designing an appropriate algorithm, the cluster can be manipulated to attain synchronization with respect to a certain value or an isolated node. Moreover, the synchronization values among various clusters vary. The main aim of this study is to investigate the asymptotic and CS problem of coupled delayed complex-valued neural network (CCVNN) models along with leakage delay in finite-time (FT). In this paper, we describe several sufficient conditions for asymptotic synchronization by utilizing the Lyapunov theory for differential systems and the Filippov regularization framework for the realization of finite-time synchronization of CCVNNs with leakage delay. We also propose sufficient conditions for CS of the system under scrutiny. A synchronization algorithm is developed to indicate the usefulness of the theoretical results in case studies.</p></abstract>

Recent advances of finite-field networks

<abstract><p>Finite-field networks (FFNs) are a class of multi-agent systems over finite fields with sensing, computing, and communication capabilities. FFNs have been investigated extensively to save computing and communication resources. This paper summarizes the current research results to provide a direction for future research. First, different models of FFNs are reviewed, including FFNs with time-delays, switching topology, and leader-following structures. Then, the consensus and synchronization problems of multi-agent systems over finite fields are analyzed, and the necessary and sufficient conditions for consensus and synchronization of some autonomous systems have been derived in recent research. Finally, the distributed control of multi-agent systems over finite fields has been developed by many scholars based on various approaches.</p></abstract>

Pinning synchronization for markovian jump neural networks with uncertain impulsive effects

This work concentrates on synchronization of neural networks (NNs) with Markovian parameters, where the Markov chain has partially unknown transition probabilities (PUTP). Due to the existence of interference and noise in practice, we combine the uncertain variable with the complex coupling term as the impulsive disturbance of NNs. A corresponding mode-dependent pinning controller is designed to reduce the control costs, and synchronization error system is also derived, whose impulsive update state is listed separately. A sufficient condition of synchronization for NNs is completed by constructing a Lyapunov functional candidate and a series of iterations. Because the disturbance should avoid being too frequent to guarantee synchronization of NNs, the allowed minimum interval h of the impulsive disturbance is derived. Finally, the correctness and the superiority of the developed result are illustrated by a numerical example.

Synchronization and adaptive control for coupled fractional-order reaction–diffusion neural networks with multiple couplings

In this paper, two kinds of coupled fractional-order reaction–diffusion neural networks (CFORDNNs) with multiple state couplings or spatial diffusion couplings are proposed. By resorting to the Laplace transform and the properties of Mittag-Leffler functions, sufficient synchronization conditions are derived for the concerned network models. In addition, to guarantee the synchronization of these two networks, several appropriate adaptive control schemes are also developed. Ultimately, the validity of the devised adaptive strategies are verified by adopting some numerical examples with simulation results.

Stability and pinning synchronization of delayed memristive neural networks with fractional-order and reaction–diffusion terms

Global asymptotic stability and synchronization are explored in this paper for fractional delayed memristive neural networks with reaction–diffusion terms (FDRDMNNs) in sense of Riemann–Liouville. First, we introduce diffusion into the existing model of fractional delayed memristive neural networks. Next, in terms of Green’s theorem and inequality technique, a less conservative criterion for the asymptotic stability of FDRDMNNs is given by endowing Lyapunov direct method. Then, the appropriate pinning feedback controllers and adaptive controllers are designed to achieve the synchronization of the FDRDMNNs, and two sufficient conditions for global asymptotic synchronization are acquired. In addition, the results based on algebraic inequalities enhance some existing ones. The numerical simulations finally verify the validity of the derived results.

Global Mittag-Leffler synchronization of coupled delayed fractional reaction-diffusion Cohen-Grossberg neural networks via sliding mode control.

This paper studies the sliding mode control method for coupled delayed fractional reaction-diffusion Cohen-Grossberg neural networks on a directed non-strongly connected topology. A novel fractional integral sliding mode surface and the corresponding control law are designed to realize global Mittag-Leffler synchronization. The sufficient conditions for synchronization and reachability of the sliding mode surface are derived via the hierarchical method and the Lyapunov method. Finally, simulations are provided to verify our theoretical findings.

Asymptotical synchronization for complex-valued stochastic switched neural networks under the sampled-data controller via a switching law

In this paper, the asymptotic synchronization problem of delayed complex-valued stochastic switched neural networks under sampled-data controller is considered. Using linear matrix inequality, switching laws and Lyapunov functional, sufficient conditions for asymptotic synchronization of the system under different controllers are obtained. Finally, an example and simulation are used to illustrate the rationality of our conclusions.

Finite-Time and Fixed-Time Synchronization of Coupled Switched Neural Networks Subject to Stochastic Disturbances

In this paper, we address the finite-time and fixed-time synchronization of a general class of switched neural networks (SNNs) with time delays subject to stochastic disturbances. Considering two types of switching in this class of SNNs: 1) intra-SNN state-dependent switching and 2) inter-SNN Markovian switching, we develop three control laws and derive three sets of sufficient conditions for both finite-time and fixed-time synchronization of SNNs subject to stochastic disturbances. We make two remarks on the effects of control-law parameters on synchronization settling time. Moreover, we derive several upper bounds of synchronization settling time and evaluate their pros and cons. Finally, we elaborate on two numerical examples to illustrate the viability of the theoretical results.

The structure of uni-directional chain for the synchronization of networked chaotic systems

In this paper, we introduce the structure of uni-directional chain (UDC) as a benchmark to probe the synchronizability of networked chaotic system. By studying the relation between the length of UDC and its synchronizability, we identify a region of coupling strength, referred to as strong controllable region (SCR), where a UDC with arbitrary length could realize synchronization that is robust to non-local disturbance. More importantly, it is found that there exists a kind of chaotic oscillators where the region of negative master stability function (MSF) overlaps with the SCR. As MSF implements local stability analysis to provide the necessary condition for the appearance of synchronization, while SCR permits stable synchronization corresponding to non-local disturbance pertinent to sufficient condition, the role of MSF for such kind of oscillator may be equivalent to provide sufficient condition of network synchronization. Besides, we propose methods for the control of network synchronization based on the characteristic of UDC. For networks with fixed structure, by obtaining a minimal spanning tree, each node chooses one of its neighbors and follows its dynamics with uniform coupling strength to realize synchronization. For growing networks, by establishing directed connection from newly added nodes to existing nodes. An interacting structure which is similar to the combination of a group of UDCs is formed and the system is guaranteed to be controlled within the SCR.

Robust secure synchronization control for multiple neural networks: An event‐triggered adaptive integral sliding mode method

AbstractThis article investigates the robust secure synchronization control of multiple neural networks (MNNs) systems with external random disturbances in the presence of actuator and sensor attacks. First, the types of attacks are analyzed in detail. Actuator attacks refers to the damage of control input signals transmitted through the network layer, and sensor attacks refers to the damage of communication channels between neural networks (NNs). Then, for the attacked NNs system, by introducing a novel neighborhood synchronization error, two novel integral sliding mode (ISM) functions with the event‐triggered mechanisms are designed. Based on this, a distributed event‐triggered adaptive ISM secure synchronization control scheme is proposed. It is worth noting that the control signal and adaptive parameters in the proposed scheme are only updated at the triggering time instants, which further saves the energy and resources consumed by the system. Next, the sufficient conditions for secure synchronization of MNNs system are obtained by constructing Lyapunov function and a positive lower bound of the internal execution time is ensured. Finally, a numerical example is given to demonstrate the effectiveness of the proposed secure synchronization control strategy.