Sufficient Conditions For Synchronization Research Articles

Synchronization of complex networks with PID pinning controller

Recently, synchronization of complex networks has been studied deeply; however, most existing works take the standard proportional control strategy approach to pinning controllers, which produces a steady-state error and has a significant time of fluctuation. In order to solve this problem, we propose a new method using the Proportional-Integral-Differential (PID) control to design a pinning control method for synchronization of complex networks. Based on Lyapunov theory, the stability of the network is proved, and sufficient synchronization conditions are obtained. Finally, examples are given to evaluate the effectiveness of the proposed PID pinning method and compare it to the traditional proportional pinning controller and adaptive pinning controller.

Sufficient synchronization conditions for resistively and memristively coupled oscillators of FitzHugh-Nagumo-type

We study the synchronization behavior of a class of identical FitzHugh-Nagumo-type oscillators under adaptive coupling. We describe the oscillators by a circuit model and we provide a sufficient synchronization condition that relies on the shape of the nonlinear conductance’s (i, u)-curve and the connectivity of the adaptive coupling network. The coupling network is allowed to be time-variant, state-dependent and locally adaptive, where we treat memristive coupling elements as a special case. We provide a physical interpretation of synchronization in terms of power dissipation and investigate the sharpness of our condition.

Cluster synchronization of stochastic two‐layer networks with infinite distributed delays via delayed pinning impulsive control

SummaryThe cluster synchronization problem of stochastic two‐layer networks with infinite distributed delays is concerned. Firstly, we study the cluster synchronization of the first layer (leader‐layer) network with the average state of each cluster of sets as synchronization target. Secondly, we design a delayed pinning impulsive controller to synchronize the second layer (follower‐layer) network to the first layer network in a mean square cluster sense. Based on stochastic impulsive analysis and Lyapunov stability theory, some sufficient conditions for cluster synchronization are obtained. Finally, the effectiveness of the theoretical results is verified through numerical simulations.

Global exponential synchronization of switching neural networks with leakage time-varying delays

In this paper, the synchronization problem of a class of switching neural networks with leakage time-varying delays is studied. A system solution-based direct analysis method is proposed to derive the sufficient conditions of global exponential synchronization for master–slave systems. Firstly, the state variable expression of the error system is derived by constructing a suitable regulation function, in which the leakage delays are explicitly transformed outside the state variable. Then, on this basis, the corresponding synchronization conditions is obtained by using the transition condition ingeniously. In addition, the obtained sufficient conditions contain only some simple linear scalar inequalities, which is different from most publications and greatly reduces the computational complexity. Finally, the reliability of the theoretical results is verified by numerical simulation. It is worth noting that the synchronization problem of switching neural networks with time-varying leakage delays is studied for the first time in this paper, and the method adopted does not need to construct any Lyapunov–Krasovskii functionals, which simplifies the proof process.

Exponential Synchronization of Complex Dynamic Networks with Time Delay and Uncertainty via Adaptive Event-Triggered Control

In this paper, exponential synchronization problem of uncertain complex dynamic networks with time delay is studied via adaptive event-triggered control. Considering the influence of external environment, a new dynamic event-triggered mechanism is proposed, in order to reduce the transmission signal among nodes and reduce the consumption of communication resources. Moreover, in the proposed control mechanism, the controller is adaptive, that is, it only works when the triggering conditions are satisfied. Then, according to the designed adaptive event-triggered control strategy, the sufficient conditions for exponential synchronization are obtained by using Lyapunov functions and inequality technique. In addition, it is proved that the system can avoid Zeno behavior. At last, using two examples to verify the feasibility of the results.

Stability analysis of synchronization in long-range temporal networks using theory of dichotomy.

Most of the previous studies on the stability analysis of synchronization in static or time-varying networks are based on the master stability function approach, which is a semi-analytical concept. The necessary and sufficient conditions for synchronization in time-varying networks are challenging problems since the last few years. We focus on the stability analysis of synchronization in time-varying networks, particularly long-range networks. The use of dichotomy theory to derive sufficient conditions for synchronization in this context is an interesting approach. The incorporation of long-range interactions adds complexity and might lead to larger regions of synchronization, providing valuable insights into the dynamics of such networks. Analyzing the co-action of the time-varying nature in the network topology and long-range interactions is a relevant and challenging task, especially when the network is not synchronized. This work appears to explore the interplay between these factors and their impact on synchronization. Additionally, the numerical study considering long-range connections governed by a power-law within the framework of an Erdös-Rényi random network is a practical way to validate and test the analytical results. It is good to see that we are exploring the effects of varying parameters such as rewiring probability, coupling strength, and power-law exponent on the synchronization state.

Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains

We present an innovative complex network of reaction–diffusion systems set in distinct domains, with boundary couplings. The complex network models the evolution of interacting populations living in a heterogeneous and fragmented habitat, whose biological individuals migrate from one patch to another. In our model, the displacements of individuals are described by mixed boundary couplings, involving both the Neumann and Robin boundary conditions, which improve the modeling of migrations by point-wise couplings. We investigate the cases of diffusion in isotropic and anisotropic habitats and establish original sufficient conditions of synchronization in this complex network model, for complete graphs, cyclic graphs and rings of nearest neighbors. In parallel, we apply our theoretical framework to a nonlinear predator–prey model with Leslie–Gower-type functional response and explore numerically the emergence of synchronization on heterogeneous Turing patterns.

Tradeoff analysis between time cost and energy cost for fixed-time synchronization of discontinuous neural networks

This article focuses on the tradeoff analysis between time and energy costs for fixed-time synchronization (FXTS) of discontinuous neural networks (DNNs) with time-varying delays and mismatched parameters. First, a more comprehensive lemma is systematically established to study fixed-time stability, which is less conservative than those in most current results. Besides, theoretical proof has proven that the upper bounds of the settling time (ST) in this article are more accurate compared to existing results. Second, on the grounds of the new fixed-time stability lemma, fixed-time synchronization problem for discontinuous neural networks with time-varying delays and mismatched parameters is explored, and sufficient conditions for fixed-time synchronization are obtained. Further, the upper bounds of energy cost during the synchronization process are estimated. Third, in order to achieve a balance between time cost and energy cost, the genetic algorithm is utilized to find the satisfactory control parameter. Finally, a numerical example is provided to verify the theoretical analysis’s correctness and the control mechanism’s feasibility.

Synchronization of multi-link and multi-delayed inertial neural networks with Markov jump via aperiodically intermittent adaptive control

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.

Relative States-Based Consensus for Sampled-Data Second-Order Multiagent Systems With Time-Varying Topology and Delays.

In this article, the consensus problem of sampled-data second-order integrator multiagent systems with switching topology and time-varying delay is studied. And, a zero rendezvous speed is not required in the problem. Two new consensus protocols that employ no absolute states are proposed, depending on the presence of delay. Sufficient synchronization conditions are obtained for both protocols. It is shown that consensus can be reached, provided there is a sufficiently small gain and periodically joint connectivity in the sense of scrambling graph or spanning tree. Finally, both numerical and practical examples are supplied for illustrative purpose, and both show the effectiveness of the theoretical results.

Synchronization of Delayed Memristor-Based Neural Networks via Pinning Control With Local Information.

In this article, a novel pinning control method, only requiring information from partial nodes, is developed to synchronize drive-response memristor-based neural networks (MNNs) with time delay. An improved mathematical model of MNNs is established to describe the dynamic behaviors of MNNs accurately. In the existing literature, pinning controllers for synchronization of drive-response systems were designed based on information of all nodes, but in some specific situations, the control gains may be very large and challenging to realize in practice. To overcome this problem, a novel pinning control policy is developed to achieve synchronization of delayed MNNs, which depends only on local information of MNNs, for reducing communication and calculation burdens. Furthermore, sufficient conditions for synchronization of delayed MNNs are provided. Finally, numerical simulation and comparative experiments are conducted to verify the effectiveness and superiority of the proposed pinning control method.

The synchronization of K-valued Fuzzy cognitive maps

Fuzzy cognitive maps (FCMs) with the abilities of knowledge representation and causal reasoning have been widely applied in the control-related fields of multi-agent systems (MAS), such as the mobile robots and unmanned aerial vehicles (UAVs). From the perspective of system applications, the cooperative control of group behaviors is a meaningful topic in this community, where the synchronization of agents is one of fundamental issues. However, how to achieve the synchronization of FCM-based control mechanism is still an open problem. In this article, two finite state fuzzy cognitive map systems with unidirectional coupling in the drive-response configuration are introduced. By utilizing matrix semi-tensor product (STP), the coupling dynamical systems are transformed into algebraic forms, based on which the necessary and sufficient conditions for complete synchronization are presented. The corresponding theoretical proofs are given and quantitative analysis are implemented. Finally, several experiments are given to prove the effectiveness of the proposed methods.

Event‐triggered delayed impulsive control for quasi‐synchronization of complex dynamic systems with packet loss and parameter mismatch

AbstractThis paper studies the event triggered delayed impulsive control strategy for quasi‐synchronization for complex dynamical systems with parameter mismatch and packet loss. By constructing a comparative lemma with time delays and Lyapunov function, a few sufficient synchronization conditions are proposed by Cauchy matrix with time delays to analyze the system. Meanwhile, the possibility of packet loss is also considered and the quasi‐synchronization of the system is investigated by using both event triggered delayed impulsive control and self‐triggered impulsive control mechanisms. Theoretical analysis results are validated by numerical simulations.

A novel fast terminal sliding mode with predefined-time synchronization

This paper aims to investigate the predefined-time synchronization analysis for two different multiple-input-multiple-output systems. Firstly, based on the definition of predefined-time synchronization, we propose a novel Lyapunov function and a novel fast terminal sliding mode, each having corresponding sufficient conditions for predefined-time synchronization. Second, we respectively derive the novel fast terminal sliding mode controllers for synchronization schemes with and without taking into account the uncertainty. The desired convergence time can be obtained by setting predefined-time parameters Tpi in advance. Finally, the controllers and the corresponding parameters designed for comparison are applied to predefined-time synchronization of two chaotic systems. The efficacy and robustness of the obtained results are demonstrated by numerical simulations.

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.