Bipartite Synchronization Research Articles

Finite‐time lag bipartite synchronization of double‐layer networks with non‐linear coupling strength and random coupling delays via T‐S fuzzy logic theory

AbstractThis article discusses finite‐time lag bipartite (FETLB) synchronization of double‐layer networks with non‐linear coupling strength and multiple time delays. The cooperative and competitive interactions between nodes are considered based on signed graphs. To address the non‐linear couplings strength, the T‐S fuzzy logic theory is used. An intermittent control approach is introduced to achieve FETLB synchronization, effectively minimizing control costs. Moreover, by the Lyapunov functional method, we derive criteria for achieving FETLB synchronization and provide estimations for the synchronization settling time. In addition, numerical simulation affirms the validity of the theoretical findings, showcasing the practical application of the synchronization results in secure communication.

Stability and bipartite synchronization of fractional-order coupled reaction–diffusion neural networks under unbalanced graph

This paper delves into the analysis of stability and bipartite synchronization (BS) in fractional-order coupled neural networks with reaction–diffusion terms (FORDNNs) under structurally unbalanced signed graphs. Central to our investigation is the novel observation in structurally unbalanced graphs without cycles, where specific nodes under particular structures are capable of achieving BS, while others maintain stability. Subsequently, for unbalanced graphs with negative rooted cycles, we present criteria that guarantee the stability of FORDNNs. Moreover, under structurally balanced graphs, sufficient conditions for achieving BS are established. A novel approach is introduced, wherein synchronization is attained without the presence of a leader node, marking a significant departure from conventional models. Finally, illustrative examples are provided, demonstrating the effectiveness and relevance of our findings.

Input–Output Finite-Time Bipartite Synchronization for Multiweighted Complex Dynamical Networks Under Dynamic Hybrid Triggering Mechanism

Abstract The problem of input–output finite-time (IO-FT) bipartite synchronization for a class of nonlinear multiweighted complex dynamical networks (CDNs) in the presence of multiple coupling delays, external disturbances, and deception attacks is explored in this study. To be precise, the limited communication resources have been mitigated with the aid of undertaken hybrid triggered strategy, which reduces the unwanted network transmission and simultaneously improves the system's performance. Specifically, in the hybrid-trigger scheme, a Bernoulli distributed random variable has been employed to switch between the two communication channels. Moreover, the event-triggered scheme involving the dynamic trigger conditions is incorporated in the sensor-to-controller, which reduces the number of triggers compared to static event-triggered strategy. Further, the adequate conditions are derived in terms of linear matrix inequalities by constructing a Lyapunov–Krasovskii functional candidate. In light of this, the required parameters involved in triggering and the gain matrix are acquired by solving the developed linear matrix inequalities. Eventually, the reliability of the developed approach is verified via the illustration of two numerical examples, including the Chua's circuit with simulation verifications.

Bipartite quasi synchronization of stochastic delayed cooperation–competition networks with gain-waving intermittent control

Given the cooperation and competition bi-directional mechanisms between subsystems, this paper aims at addressing bipartite quasi synchronization (BQS) of stochastic delayed cooperation–competition networks (SDCNs). We propose a gain-waving intermittent control policy, that includes more of the existing works, to assist the BQS, in an effort to cope with external interferences and the possibility of actuator damage caused by rapid switching. Intermittent gain is to be quantized legitimately via the postulate of waving average gain. Within this context, novel Lyapunov inequalities concerning bounded waving gain and unbounded one are advanced to ensure the BQS of SDCNs in conjunction with graph theory, since the present differential inequalities are incapable of being inoperative. Then we develop two kinds of BQS criteria and the bounds for the BQS error are estimated where the scenarios of bounded waving gain and unbounded one are involved separately. Besides, corresponding criteria about complete bipartite synchronization are presented and several design methods of gain-waving intermittent control are introduced by specific examples. Finally, the validity of the theoretical results is examined by an application on Chua’s circuit with numerical simulations being shown.

Bipartite synchronization for coupled memristive neural networks: Memory-based dynamic updating law

In this paper, bipartite synchronization for memristive neural networks with multi-delay couplings is investigated. The evaluation index of unbounded coupling delays on synchronization could be quantitatively analyzed by considering proportional delay, which will undoubtedly and strongly impede synchronous behavior. By simultaneously taking synchronization and anti-synchronization patterns into account, a novel impulsive controller with a signed form is elaborately designed. For the purpose of selecting suitable impulsive instants, a dynamic self-triggered mechanism is introduced. Additionally, to mitigate the possible risk of the dynamic mechanism transitioning into a static mechanism in exceptional scenarios, a memory-based adaptive updating law is therefore proposed in this paper. It should be noted that the adaptive control related dynamic parameters considered in this paper are in a non-monotonic form. By utilizing Lyapunov stability theorem, parameter variation approach and contradiction analysis method, sufficient conditions for ensuring the synchronization are successfully derived. Finally, two experiments are presented to demonstrate the practicability of the derived results.

Bipartite Synchronization of Signed Networks With Time-Vary Delays Based on T-S Fuzzy System

Bipartite Synchronization of Signed Networks With Time-Vary Delays Based on T-S Fuzzy System

Practical Fixed-Time Bipartite Synchronization of Uncertain Coupled Neural Networks Subject to Deception Attacks via Dual-Channel Event-Triggered Control.

This article investigates the practical fixed-time synchronization of uncertain coupled neural networks via dual-channel event-triggered control. Contrary to some previous studies, the bipartite synchronization of signed graphs representing cooperative and antagonistic interactions is studied. The communication channel is introduced into deception attacks, which are described by Bernoulli's stochastic variables. Based on the concept of two channels, event-triggered mechanisms are designed for sensor-to-controller and controller-to-actuator channels to reduce communication consumption and controller update consumption as much as possible. Lyapunov and comparison theories are used to derive synchronization criteria and explicit expression of settling time. An example of Chua's circuit system is presented to demonstrate the feasibility of the obtained theoretical results.

Fixed-Time Bipartite Synchronization of a Signed Graph: An Economical and Practical Strategy

Fixed-Time Bipartite Synchronization of a Signed Graph: An Economical and Practical Strategy

Fixed-Time Aperiodic Intermittent Control for Quasi-Bipartite Synchronization of Competitive Neural Networks.

This paper concerns a class of coupled competitive neural networks, subject to disturbance and discontinuous activation functions. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results.

Bipartite Synchronization of Fractional Order Multiple Memristor Coupled Delayed Neural Networks with Event Triggered Pinning Control

This paper investigates the leader and leaderless bipartite synchronization with the signed network utilizing the model of multiple memristor and coupled delayed neural network in an event-triggered pinning control. The usage of the descriptor method in fractional-order neural networks in case of a non-differentiable delay can be seen in this paper. Further, Lyapunov functional criteria, including Lur’e Postnikov Lyapunov functional, is established, and bipartite leader and leaderless synchronization are proved. The obtained numerical results can be seen as accurate to the theoretical results.

Event-triggered hybrid impulsive control for synchronization of fractional-order multilayer signed networks under cyber attacks

In this paper, we consider the exponential bipartite synchronization (EBS) problem of fractional-order multilayer signed networks with time-varying delays (FO-MSNT) under random cyber attacks. In contrast to the existing literature, the proposed hybrid event-triggered controller combines the advantages of feedback controller and impulsive controller, and the event-triggered condition is constructed by applying the network topology and the Lyapunov function of the subsystem, rather than the state function of the subsystem. Based on the Lyapunov–Razumikhin method and the graph theory, some sufficient conditions for achieving EBS of FO-MSNT under cyber attacks which are related to the topology of networks, the event-triggered parameters, the order of fractional derivative and the signal sent by the enemy are obtained. Furthermore, fractional-order coupled Chua’s circuits model and fractional-order power systems built on MSNT are established and the EBS issues under cyber attacks are analyzed. Numerical examples and simulations are provided to show the validity of our theories.

Coopetition-dependent controller design for bipartite synchronization of cooperation–competition delayed memristive neural networks

In this paper, the bipartite synchronization problem for cooperation–competition delayed memristive neural networks (CCDMNNs) is addressed via designing a coopetition-dependent controller. Based on the coordinate transformation technique, an easy-to-analyze error system is constructed in the presence of cooperation–competition interactions. Two control strategies are proposed respectively to realize bipartite synchronization. First of all, a coopetition-dependent controller that can eliminate the impact of cooperation–competition interactions as well as the time-varying state-dependent memristive connection weights is designed. In combination with inequality techniques, the Lyapunov theory and the interval matrix method, an LMI-form criterion is established to ensure the bipartite synchronization of CCDMNNs. Moreover, an adaptive controller that can automatically adjusts the control parameters to achieve appropriate control gains is proposed to further improve the control performance. Finally, a numerical example is given to verify the correctness and superiority of the proposed control schemes.

Quantized dynamic event-triggered control for fixed/preset-time bipartite synchronization of memristor-based discontinuous multi-layer signed networks

This study addresses the fixed/preset-time bipartite synchronization (FTBS/PTBS) of memristor-based discontinuous multi-layer signed networks via quantized dynamic event-triggered control (ETC). Firstly, a memristor-based neural network model incorporating multi-layer coupling structures, signed networks and discontinuous activations is built. Subsequently, by designing two quantized dynamic ETC strategies without the linear feedback term, the FTBS and PTBS of the considered networks are discussed, and it is proved that Zeno behavior can be ruled out. In contrast to the previous static ETC mechanism, the introduced internal dynamic variable can significantly decrease the triggering times and further save communication resources. Lastly, three numerical examples are offered to verify the correctness and practicability of the theoretical analysis.

Event-Triggered Bipartite Synchronization of Delayed Inertial Memristive Neural Networks With Unknown Disturbances

Event-Triggered Bipartite Synchronization of Delayed Inertial Memristive Neural Networks With Unknown Disturbances

Bipartite leaderless synchronization of fractional-order coupled neural networks via edge-based adaptive pinning control

This paper introduces the signed graph into fractional-order coupled neural networks (FCNNs) and the bipartite synchronization is investigated for leaderless FCNNs. Instead of formulating leader’s state or isolated node’s state as the synchronization reference target, the bipartite synchronization of leaderless FCNNs is discussed by developing a direct error approach. First, an important fractional-order inequality is rigorously proved by contradiction. By virtue of fractional-order inequality, gauge transformation and several analytical tools, the criteria of bipartite leaderless synchronization are obtained for FCNNs with heterogeneous and homogeneous coupling weights. Specially, for the two types coupling weights, the adaptive pinning schemes are adopted which just rely on partial network information based on the spanning tree and connected dominating set, respectively. Eventually, the theoretical analysis is verified by two numerical simulations.

Finite‐time bipartite synchronization of T–S fuzzy coupled neural networks via quantized adaptive control

AbstractBased on the framework of signed graphs, this paper investigates the finite‐time (FET) bipartite synchronization of Takagi‐Sugeno (T–S) fuzzy coupled neural networks with output coupling and state‐dependent parameters. Adaptive control schemes with quantizer are designed, and generalized norm is considered. Based on the framework of bipartite synchronization and FET synchronization, several sufficient conditions are established to realize the goal of synchronization by using Lyapunov functional method. Moreover, some numerical simulations are provided to illustrate the theoretical results.

Interval Bipartite Synchronization of Multiple Neural Networks in Signed Graphs.

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

Bipartite synchronization of multilayer signed networks under aperiodic intermittent-based adaptive dynamic event-triggered control

This article addresses the exponential bipartite synchronization (EBS) of multilayer signed networks with time-varying coupling (MSNs) under aperiodic intermittent-based adaptive dynamic event-triggered control (AAIDETC). Firstly, to increase the elasticity, a novel AAIDETC strategy is presented, whose superiority is that the control gains and the triggering parameters can vary with the evolution of the considered networks. Meanwhile, concerning the aperiodic intermittent control, a new definition of average control ratio (ACR) is put forward, which is more rigorous compared with the relevant results. Then, by the method of ACR, graph theory and Lyapunov approach, the simpler synchronization criterion is gained, which avoids the topology structure of MSNs. Moreover, the EBS issues of Chua’s circuits and neural networks established on MSNs are studied, which are two practical applications of our theoretical results. Finally, corresponding numerical simulations are presented to verify the availability of the obtained results.

Bipartite secure synchronization for dynamic networks under deception attacks via delay-dependent impulsive control

In this paper, we investigate mean-square bounded bipartite synchronization of coupled dynamic networks subject to deception attacks, especially under directed/undirected signed interconnection structures. An impulsive secure control input involving stabilizing delays is proposed. The average impulsive delay (AID) method is used to fetch the information of time delay existing in impulses, and then this information is effectively integrated to mitigate the negative effects of deception attacks on synchronization. A concept of stochastic variables is introduced to serve as a measure of attack success when delayed impulsive control signals are replaced with false data from the impulsive controller-to-actuator. To achieve desired synchronization performance under deception attacks, the gains of pinning impulsive control, the average impulsive interval (AII), AID and the attack intensity are co-designed. An upper bound for synchronization errors is provided, which can be adjusted with multiple adjustable parameters. In addition, the AII and AID methods are used to remove the restriction on upper/lower bounds of two consecutive impulsive instants. Finally, numerical examples are given to illustrate the validity of the theoretical results.

Security bipartite synchronization of MASs resilient to DoS attacks

This paper considers the security bipartite synchronization problem of nonlinear multi-agent systems (MASs) under the impact of denial-of-service (DoS) attacks. Notice that malicious attackers may block the neighbor information transmission among agents, which will reduce the efficiency of the distributed control strategy and even paralyze the entire system. In order to eliminate the impact of DoS attacks on the stability of MASs, this paper represents the first attempt to solve the security bipartite synchronization problem with the help of a distributed leader state observer. An observer that can obtain the leader state estimation is established, and the control strategy constructed based on the observer can eliminate the impact of DoS attacks. Theoretical analysis shows that the control strategy proposed in this paper can realize the security bipartite synchronization of the system under the impact of DoS attacks. The validity of the proposed results is verified by several presented simulation results.