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This work investigates the bipartite synchronization issue of a network of nonlinear dynamic systems with aperiodic data-sampling, and the underlying topology follows a changeable signed graph. In order to achieve the control objective, some event-triggered protocols are developed based on sampled data, and some theorems are derived, which elucidate how the system dynamics, network topology, triggering parameters and sampling periods decide synchronization, affirming the critical impact of the average value of the algebraic connectivity of an induced unsigned graph over certain intervals. Unlike most existing works on periodic event-triggered control, the triggering mechanism herein is based on aperiodic sampled data, which thus provides more flexibility for practical use. Meanwhile, the topology is allowed to alter either discretely or continuously, exhibiting good applicability. Finally, some numerical examples are given to validate the theoretical results and demonstrate the performance of our design. [ABSTRACT FROM AUTHOR]

Based 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper studies the problem of under what conditions the general nonlinear networks with directional competition and perturbations to achieve fully distributed BS (bipartite synchronization). For the norm bounded disturbances with unknown upper bound, under the assumption that the signed digraph is structurally balanced and contains a directed spanning tree, a fully distributed observer-based adaptive protocols is designed for BS problem of general nonlinear networks with no leader and neural networks approximation. For the disturbances generated by exosystems, based on a disturbance observer, a fully distributed disturbance observerbased adaptive protocol is proposed to make network achieve bounded BS. In order to reduce the chattering phenomenon, some adaptive gains and adaptive parameter vector of neural networks approximation are proposed. Finally, the theoretical results are verified by two numerical simulation examples. [ABSTRACT FROM AUTHOR]

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. • A new MSN model with time-varying coupling is proposed. • A novel AAIDETC is developed. • An improved definition of average control ratio is presented. [ABSTRACT FROM AUTHOR]

This literature mainly concerns finite-time bipartite synchronization (FTBS) of networked systems (NSs) with time-varying and random coupling delays based on signed graphs. Via Bernoulli random variables, NSs will switch between the delayed coupled systems and coupled systems without time delays. Two kinds of quantized controllers are constructed to realize the goal of synchronization. Different from many existing finite-time stability results established by the classical finite-time stability theorem, the results of this paper are obtained directly based on 1-norm analytical method. Numerical examples are employed to verify the presented results. [ABSTRACT FROM AUTHOR]

This paper addresses the bipartite synchronization of multi-agent systems with time-varying delays and signed graph under deception attacks, where the systems contain both the self-structure delayed term and the coupling delayed term. The deception attacks are assumed to be randomly launched at each impulse instant. By using the gauge transformation, Lyapunov function method, Halanay differential inequality and linear matrix inequality techniques, several sufficient conditions are newly established to guarantee the achievement of bipartite synchronization, in which some special cases of multi-agent systems without delay or deception attacks are further considered. Two numerical examples are provided to illustrate the effectiveness of the proposed results. Finally, a new multi-agent speech communication system is constructed based on the bipartite synchronization of the multi-agent systems, where two agents for point-to-point communication can generate synchronous chaotic encryption/decryption key streams. The experimental results show that the proposed multi-agent speech communication system has the advantages of high security against some classical attacks.

Based on the framework of signed graphs, we investigate finite-time bipartite synchronization (FTBS) of delayed complex-valued complex networks (DCVCN) in this paper. Several control strategies with quantizer are designed, which can save communication resources. 1-norm analytical techniques are used and developed to present strict proof of theoretical results. Some FTBS criteria are established by use of multiple Lyapunov functions, and the settling time is estimated by means of control parameters and initial values. Numerical simulation results are given to verify the validity of theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the prespecified-time bipartite synchronization (PTBS) of coupled reaction-diffusion memristive neural networks (CRDMNNs) with both competitive and cooperative interactions. Two types of bipartite synchronization are considered: leaderless PTBS and leader-following PTBS. With the help of a structural balance condition, the criteria for PTBS for CRDMNNs are derived by designing suitable Lyapunov functionals and novel control protocols. Different from the traditional finite-time or fixed-time synchronization, the settling time obtained in this paper is independent of control gains and initial values, which can be pre-set according to the task requirements. Lastly, numerical simulations are given to verify the obtained results.

In this paper, the bipartite synchronization of signed Lur'e network is studied under intermittent control, where the communication relationship of these adjacent nodes in the network can be either cooperative or competitive. Assuming that the network is structurally balanced, bipartite synchronization can be reached with some conditions and coordinate transform criterion. Then, Based on Lyapunov stability theory, some important norms are established. Ultimately, the simulation results can illustrate validness of theoretical analysis. • Based on the features of coordinate control, Lur'e networks is utilized to study synchronization problem. And synchronizing all nodes is the ultimate goal by adopting coordinate transform and nonlinear function. • Intermittent and pinning algorithm are used to achieve synchronization in signed Lur'e networks. Pinning control is a control strategy, which only needs to control finite nodes of the system [1]. Thus it is proposed to achieve bipartite leader-following synchronization in networks. • Finally, a numerical example is given to demonstrate the effectiveness and feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

Recently, passivity of fractional complex networks has aroused much interest, but the concerned models contain only cooperative relationships and the competitive interaction among individuals is ignored. In this article, a class of fractional complex networks with a signed graph is considered and several conditions are derived to achieve the passivity of fractional signed networks by pinning strategies designed based on M-matrix theory. Particularly, in pinning adaptive control schemes, the pinning nodes are selected only according to the cooperative relationships among nodes and the control gains can regulate automatically to meet the actual demand. In addition, without translating the signed networks into corresponding unsigned networks based on the gauge transformation, some criteria of bipartite synchronization for fractional signed networks are obtained based on the feature of the signed topology and the derived passivity results. The theoretical results are eventually verified by several illustrate examples. • Competitive interaction is considered in the passivity and synchronization of fractional networks. • A direct analysis method is developed to explore passivity and bipartite synchronization. • Pinning schemes are designed by cooperation and control gains are determined by competitive relations. [ABSTRACT FROM AUTHOR]

This work concentrates on the issue of leader-following bipartite synchronization of multiple memristive neural networks with Markovian jump topology. In contrast to conventional coupled neural network systems, the coupled neural network model under consideration possesses both cooperative and competitive connections among neuron nodes. Specifically, the interaction between neighbors' nodes is described by a signed graph, in which a positive weight represents an alliance relationship between two neuron nodes while a negative weight represents an adversarial relationship between two neuron nodes. By designing a pinning discontinuous controller that makes full use of the mode information, some effective criteria that ensure the stability of bipartite synchronization error states are obtained. All network nodes can synchronize the target node state bipartitely. Finally, two simulation examples are provided to demonstrate the viability of the suggested bipartite synchronization control approach. [ABSTRACT FROM AUTHOR]

The problem of bipartite synchronization is addressed for discrete-time networks with antagonistic interactions via hybrid control with impulsive effects. Firstly, a hybrid state-feedback controller, which combines a pinning state-feedback controller and an impulsive state-feedback controller, is presented, and the criterion of the bipartite synchronization is derived by applying the average impulsive interval method. Secondly, for the case of the network states not all being measured, a hybrid measurement-feedback controller, which combines a pinning measurement-feedback controller and a pinning impulsive measurement-feedback controller, is proposed. The time-varying Lyapunov function method is utilized to design the hybrid measurement-feedback controller such that the bipartite synchronization is realized. Finally, some numerical simulations are performed to illustrate the efficiency of the proposed controller design methods. [ABSTRACT FROM AUTHOR]

In this paper, without converting the second-order inertial neural networks (INNs) into a first-order differential system by introducing variable substitution, the problem of passivity-based bipartite synchronization in a signed network composed by an array of coupled INNs with time-varying delay is investigated via quantized pinning control. By choosing an appropriate Lyapunov–Krasovskii functional (LKF), applying Jensen inequality and reciprocally convex inequality to estimate the derivative of the LKF, several sufficient conditions, which guarantee the bipartite leader-following synchronization for the coupled INNs with time-varying delay, are newly obtained in terms of linear matrix inequalities (LMIs). When the quantization is not considered in the pinning controller, the criterion of bipartite leader-following synchronization in terms of low-dimensional LMIs is established by using the properties of M-matrices. And the criterion of bipartite leaderless synchronization in terms of low-dimensional LMIs is also proposed by a matrix U. A numerical example is provided to demonstrate the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

This work examines the practical prescribed-time bipartite synchronization problem of some interacting neural networks under the leaderless and leader-follower framework, respectively, where the topological structure follows certain signed graph. By applying a feedback controller with well-designed high-gain function, the practical bipartite synchronization is proved to be achievable when time approaches certain prescribed-time. Our theorems provide simple criteria for designing the control parameters and reveal the impact of the underlying network. An interesting finding is that, under a leader-follower framework, bipartite synchronization is unachievable under the conventional pinning controller if the followers that can reach the leader belong to different sets of the signed graph. Furthermore, despite the use of increasing control gain, the control signals are shown to remain bounded. Finally, some numerical examples are presented to show the theoretical result's validity. [ABSTRACT FROM AUTHOR]

This paper investigates the bipartite synchronization of memristor-based fractional-order coupled delayed neural networks with structurally balanced and unbalanced concepts. The main result is established for the proposed model using pinning control, fractional-order Jensen's inequality, and the linear matrix inequality. Further, new sufficient conditions are derived using the Lyapunov–Krasovskii functional with delay-dependent criteria. Finally, numerical simulations are provided including two numerical examples to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this work, an adaptive controller, formulated as linear feedback controls plus nonlinear parts, is synthesized to achieve bipartite leader-following synchronization of delayed incommensurate fractional-order memristor-based neural networks (FMNNs), in which follower FMNNs are linearly coupled under a signed digraph. The salient features of this research lie in two aspects: (1) the assumption on time-varying delays is very weak, since it neither requires boundedness of delays nor restricts the differentiation of time delay functions; (2) the adaptive controller contains no delay term, and it is feasible for both bounded and unbounded activation functions. As the preparatory work for stability analysis of the controlled synchronization error system, the ready-made results on delayed incommensurate fractional-order linear positive systems, especially stability condition and comparison principle, are perfected by relaxing premises of time-varying delays. Besides, a group of differential inclusion inequalities are established as a powerful aid in scaling the bipartite synchronization error system. More relevantly, an algebraic synchronization criterion, formulated in terms of coupling strength, inner coupling matrix, Laplacian matrix and FMNN system parameters, is proved with the benefit of vector Lyapunov function and positive system theory. With the controller utilized, linear feedback controls can be exerted merely on partial neurons of some selected FMNNs, which is exemplified by numerical simulations. [ABSTRACT FROM AUTHOR]

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. • Synchronization patterns and anti-synchronization patterns in some previous works could be thought as one of the special cases in our paper. • A non-monotonic dynamic updating law is devised by incorporating memory information, specifically utilizing the sparse historical states of nodes. • Lower bound of dynamic parameter is proved to be greater than a specific positive scalar in this work, that is, the importance of the role played by the dynamic parameter in determining impulsive intervals is enhanced. [ABSTRACT FROM AUTHOR]

In this paper, bipartite synchronization of signed networks with stochastic disturbances via aperiodically intermittent control is investigated. The aperiodically intermittent control presented is based on discrete-time state observations rather than continuous-time ones. To formulate signed networks and exhibit the competitive relation, a structurally balanced signed network is built and all the units are divided into two subcommunities. By employing Lyapunov method and graph theory, some sufficient conditions on bipartite synchronization are given. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control and feedback control respectively, two corollaries are also provided to ensure the bipartite synchronization of the signed networks. Ultimately, two applications to coupled single-link robot arms and coupled oscillators are presented and corresponding numerical examples are respectively provided to verify the feasibility and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

For the structurally balanced and structurally unbalanced graphs, two new fixed-time control protocols were designed to ensure the bipartite synchronization for coupled delayed neural networks with external disturbances. According to the fixed-time stability theory and some inequality skills, some sufficient criteria were obtained to guarantee the coupled network to reach bipartite synchronization in fixed time, and the upper-bounds of the settling time were estimated. The robustness and the disturbance rejection were verified. To improve the applicability of the considered network models, the considered activation functions were discontinuous, and the differential inclusion and set-valued Lie derivative theories were used to handle with the discontinuous systems. The numerical simulations were proposed for the fixed-time bipartite synchronization of coupled delayed neural networks under the structurally balanced and structurally unbalanced graphs, respectively. The results show that the effectiveness of the control algorithm and the validity of the theoretical results are verified. [ABSTRACT FROM AUTHOR]

In this paper, the bipartite synchronization issue for a class of coupled reaction–diffusion networks with antagonistic interactions and switching topologies is investigated. First of all, by virtue of Lyapunov functional method and pinning control technique, we obtain some sufficient conditions which can guarantee that networks with signed graph topologies realize bipartite synchronization under any initial conditions and arbitrary switching signals. Secondly, for the general switching signal and periodic switching signal, a pinning controller that can ensure bipartite synchronization of reaction–diffusions networks is designed based on the obtained conditions. Meanwhile, a directed relationship between coupling strength and control gains is presented. Thirdly, numerical simulation is provided to demonstrate the correctness and validity of the derived theoretical results for reaction–diffusion systems. We briefly conclude our findings and future work. [ABSTRACT FROM AUTHOR]

This paper addresses the bipartite leader-following and leaderless synchronization in a signed network composed by an array of coupled Lurie systems with time-varying delay, where the signed network contains both the non-delay coupling term and the delay coupling term. By using the pinning control strategy and a gauge transformation to transform the problem of bipartite synchronization for signed network into that of synchronization of unsigned network, choosing an appropriate Lyapunov–Krasovskii functional (LKF), applying Jensen inequality and reciprocally convex inequality to estimate the derivative of the LKF, several sufficient conditions, which guarantee the bipartite leader-following and leaderless synchronization for the coupled Lurie networks with time-varying delay, are newly obtained in terms of linear matrix inequalities (LMIs). When the delay coupling term is not considered, some criteria in terms of low-dimensional LMIs are established by using M-matrix theory. A numerical example is provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The bipartite synchronization problem for fractional order antagonistic coupled neural networks (FACNNs) is investigated in this paper. Using the properties of gamma function and special matrix, some criteria for bipartite Mittag–Leffler (M–L) synchronization and bipartite finite time synchronization of FACNNs have been obtained. To achieve bipartite finite time pinning synchronization, hybrid control strategy is designed. That is, finite time control combined with pinning control, pinning partial nodes, which can access the information of the leader. The upper bound of synchronization setting time is obtained. [ABSTRACT FROM AUTHOR]

This paper considers the finite-time and fixed-time bipartite synchronization (FFTBS) of coupled delayed neural networks (CDNNs) under signed graphs. For the structurally balanced or unbalanced network topology, both the goals of FFTBS of CDNNs are achieved simultaneously by a unified discontinuous controller. Some sufficient criterion are obtained to ensure the FFTBS under the new designed protocols, and the corresponding settling times are estimated as well. Finally, two simulations are established to verify the validity and effectiveness of the designs. [ABSTRACT FROM AUTHOR]

The study investigates bipartite synchronization of inertial coupled delayed neural networks (ICDNNs) with signed digraph by non-reduced order method and pinning control. The second-order CDNNs will not be converted into a first-order differential system by introducing variable substitution. Instead, a novel Lyapunov–Krasovskii functional is proposed which depends on the topology of the ICDNNs. Some sufficient conditions for linear matrix inequalities (LMI) are derived to realize bipartite synchronization, which is based on matrix decomposition theory and Barbalat Lemma in strongly connected signed networks. And then, M-matrix theory is utilized to generalize the results to networks containing directed spanning trees. Finally, two examples are used to verify the validity of the derived theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the bipartite synchronization problem of coupled inertia memristor-based neural networks with both cooperative and competitive interactions. Generally, coopetition interaction networks are modeled by a signed graph, and the corresponding Laplacian matrix is different from the nonnegative graph. The coopetition networks with structural balance can reach a final state with identical magnitude but opposite sign, which is called bipartite synchronization. Additionally, an inertia system is a second-order differential system. In this paper, firstly, by using suitable variable substitutions, the inertia memristor-based neural networks (IMNNs) are transformed into the first-order differential equations. Secondly, by designing suitable discontinuous controllers, the bipartite synchronization criteria for IMNNs with or without a leader node on coopetition networks are obtained. Finally, two illustrative examples with simulations are provided to validate the effectiveness of the proposed discontinuous control strategies for achieving bipartite synchronization. [ABSTRACT FROM AUTHOR]

Investigating the prescribed-time synchronization problem for multiple linear agents is challenging because the states and inputs of the system are coupled through the state-input matrix pair. To address this challenge, this paper develops a gain scheduling strategy for linear multi-agent systems over a cooperative-antagonistic network. First, the strategy converts the problem to a time-varying parameter design problem using a time-varying parametric Lyapunov equation (TVPLE). By exploiting the time-varying solution to TVPLE for designing the feedback gains, prescribed-time bipartite synchronization protocols are designed for systems over undirected and directed networks, respectively. These protocols require some global information; therefore, edge- and node-based adaptive gain scheduling strategies are further developed to achieve the prescribed-time bipartite synchronization in a fully distributed manner, which guarantees simultaneous convergence of both state synchronization and adaptive gains within a prescribed time. Finally, a simulation example is presented to demonstrate the effectiveness of the designed adaptive protocols. [ABSTRACT FROM AUTHOR]

In this paper, the bipartite state synchronization problem of heterogeneous multi-agent systems (MASs) with active leader under adversarial signals over signed digraph is studied. The non-zero control of active leader is bounded, and we can update this control to protect followers from possible danger. Firstly, the bipartite state synchronization problem over signed digraph is converted to a regular tracking synchronization problem over nonnegative digraph after state transformations for heterogeneous MASs with active leader under adversarial signals. Then, novel distributed observers are designed to estimate the state of leader, as well as prevent disrupted data of agent from propagating the communication networks. Observer-based H ∞ optimal controllers are also designed for each follower to mitigate effects on disrupted agents that agents under attack, and the inhomogeneous algebraic Riccati equations (AREs) are obtained. Meanwhile, a data-based off-policy reinforcement learning (RL) algorithm is used to solve the AREs without requiring the dynamics of agents. At last, the effectiveness of the algorithm is demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

Summary: This paper considers the bipartite leaderless and leader‐following synchronization in a network of coupled Lur'e systems with sector‐condition node dynamics and signed digraph topology, where the interaction digraph consists of both positive and negative communication links. Continuous‐time and sampled‐data control algorithms are, respectively, proposed to solve the bipartite synchronization problems for the signed Lur'e network. Under some assumptions on the network structure and node functions, some bipartite synchronization conditions are established for signed Lur'e network by using coordinate transform, linear matrix inequalities, and algebraic graph theories. For the continuous‐time control algorithms, it is shown that the bipartite synchronization problems of the signed Lur'e network can always be solved if the coupling strength is sufficiently large and the network topology satisfies some suitable conditions. For the sampled‐data control algorithms, an upper bound of the sampling intervals is estimated to ensure that the bipartite synchronization can be reached in the signed Lur'e network. Some simulation results are given to illustrate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract This paper considers the bipartite leader-following synchronization in a signed network composed by an array of coupled delayed neural networks by utilizing the pinning control strategy and M-matrix theory, where the communication links between neighboring nodes of the network can be either positive or negative. Under the assumption that the node-delay is bounded and differentiable, a sufficient condition in terms of a low-dimensional linear matrix inequality is derived for reaching bipartite leader-following synchronization in the signed network, based on which a simple algebraic formula is further given to estimate an upper bound of the node-delay. When the node-delay is bounded and non-differentiable, some criteria are established by using the descriptor method and the reciprocally convex approach such that the bipartite leader-following synchronization problem for the signed network can be successfully solved. Finally, numerical simulations are provided to illustrate the effectiveness of theoretical analysis. Highlights • Address bipartite synchronization of CDNNs under signed graph and pinning control. • Derive simple bipartite synchronization criteria for CDNNs with differentiable delay. • Provide bipartite synchronization criteria for CDNNs with non-differentiable delay. [ABSTRACT FROM AUTHOR]

The paper investigates bipartite synchronization (BS) and bounded bipartite synchronization (BBS) of a network of identical linear systems with antagonistic interactions and time-varying topologies. When at each time instant all agents can be divided into two hostile camps, and the members of two hostile camps are unchanged as time goes on, we obtain some sufficient conditions for bipartite synchronization under mild assumption that the signed graph is uniformly quasi-strongly connected. When the members of hostile camps are changed as time goes on, or at some time instants all agents cannot be divided into two hostile camps, we consider this network as a perturbation of a particular network which can achieve bipartite synchronization. We obtain some sufficient conditions such that the network achieves bounded bipartite synchronization. Finally, we present two numerical examples to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This dissertation mainly discusses the fast fixed-time bipartite synchronization (FFDT-BS) of TS fuzzy complex networks (TS FCNs) with signed graphs under impulsive control, where the communications between adjacent nodes are both cooperative and competitive. Different from most control protocol, the control process can be divided into two steps (impulsive control before settling time T and fixed-time control after T), and both the impulsive controller and FFDT controller are designed as fuzzy logic systems. By adopting impulsive control theory and mathematical induction, and constructing comparison system, some novel sufficient criteria are presented to guarantee the FFDT-BS of the TS FCNs within bounded time independent of the initial conditions. It is noting that the bipartite synchronization achieves faster convergence than most existing results, which is more practical and efficient. The performance comparisons of pure impulsive control, pure FFDT control, exist both impulsive control and FFDT control demonstrate the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper studies the synchronization phenomena in a network of heterogeneous nonlinear systems over signed graph, which can be considered as the perturbation of a network of homogeneous nonlinear systems. Assume that the signed graph is structurally balanced, the nonlinear system satisfies one-sided Lipschitz condition, and a leader pins a subset of agents. Under some proper initial conditions of the leader, we derive some conditions under which bipartite synchronization error can be kept arbitrary small by choosing a proper pining scheme. This property is called practical pinning bipartite synchronization as an alternative synchronization notion for network of heterogeneous nonlinear systems over signed graph. Finally, we present a numerical example to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper addresses the bipartite synchronization of coupled multi-order fractional neural networks (MFNNs) with time-varying delays. An effective event-triggered controller is proposed, and sufficient criteria for ensuring the bipartite synchronization are derived by using the Lyapunov function in vector form and the comparison principle for multi-order fractional differential equations. In addition, the preclusion of Zeno behavior is discussed. The results obtained in this paper cover the bipartite synchronization of both fractional neural networks with identical order and integer-order neural networks as special cases. A numerical example is given to verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, the issue of bipartite synchronization for coupled delayed neural networks (CDNNs) with cooperative-competitive interaction is firstly investigated via event-triggered control (ETC) mechanism, which greatly reduces communication bandwidth and computational burden. Firstly, in virtue of the signed graph theory, the model of CDNNs with cooperative-competitive interaction is established. Next, under the designed event-triggered controller, statical event-triggered control (SETC) condition and dynamical event-triggered control (DETC) condition for realizing bipartite synchronization of CDNNs are derived separately by utilizing Lyapunov functional method. Furthermore, an algebraic formula is provided to calculate the positive lower bound of the trigger interval, which indicates that Zeno-behavior does not arise. At last, the feasibility of the proffered ETC to realize bipartite synchronization is further demonstrated by an illustrative example. • Bipartite synchronization of delayed cooperative-competitive neural networks was studied. • Novel event-triggered theme is designed to decrease the control cost. • The trigger threshold is simpler than some existing results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the prespecified-time bipartite synchronization (PTBS) of coupled reaction-diffusion memristive neural networks (CRDMNNs) with both competitive and cooperative interactions. Two types of bipartite synchronization are considered: leaderless PTBS and leader-following PTBS. With the help of a structural balance condition, the criteria for PTBS for CRDMNNs are derived by designing suitable Lyapunov functionals and novel control protocols. Different from the traditional finite-time or fixed-time synchronization, the settling time obtained in this paper is independent of control gains and initial values, which can be pre-set according to the task requirements. Lastly, numerical simulations are given to verify the obtained results.