Adaptive exponential cluster synchronization in colored community networks via aperiodically intermittent pinning control

This paper investigates the problem of pinning cluster synchronization for colored community networks via adaptive aperiodically intermittent control. Firstly, a general colored community network model is proposed, where the isolated nodes can interact through different kinds of connections in different communities and the interactions between different pair of communities can also be different, and moreover, the nodes in different communities can have different state dimensions. Then, an adaptive aperiodically intermittent control strategy combined with pinning scheme is developed to realize cluster synchronization of such colored community network. By introducing a novel piecewise continuous auxiliary function, some globally exponential cluster synchronization criteria are rigorously derived according to Lyapunov stability theory and piecewise analysis approach. Based on the derived criteria, a guideline to illustrate which nodes in each community should be preferentially pinned is given. It is noted that the adaptive intermittent pinning control is aperiodic, in which both control width and control period are allowed to be variable. Finally, a numerical example is provided to show the effectiveness of the theoretical results obtained.     

Pinning synchronization for directed networks with node balance via adaptive intermittent control

In this paper, the problem of synchronization control for directed networks with node balance is investigated. First, a dynamical model of directed network is proposed. Additionally, a new adaptive intermittent scheme is introduced to realize pinning synchronization and some novel criteria are derived by constructing a piecewise auxiliary function and utilizing piecewise analysis method and the theory of series. Based on those criteria, a feasible bound of the rate of control time is given. Finally, some examples with numerical simulations are given to demonstrate the effectiveness of the results derived.

     

The synchronization of general complex dynamical network via pinning control

In this paper, the globally synchronization of the general complex network is investigated. Firstly, we discuss the synchronization problem of the linearly coupled and directed network under the pinning control, and make comparison with the previous work about the undirected network. Sufficient conditions are obtained to guarantee the realization of synchronization. Secondly, the synchronization problem of nonlinearly coupled and undirected network under the pinning control is studied, and a criteria of getting synchronization is given. Furthermore, we introduced the adaptive adjustment of the coupling strength in nonlinearly coupled network. At last, we give simulation examples to verify our theoretical results.     

New results on synchronization of chaotic systems with time-varying delays via intermittent control

This paper is concerned with the problem of exponential synchronization for chaotic systems with time-varying delays by using periodically intermittent control. Some new and useful synchronization criteria are obtained based on the differential inequality method and the analysis technique. It is noteworthy that the methods used in this paper are different from the techniques employed in the existing works, and the derived conditions are less conservative. Especially, a strong constraint on the control width that the control width should be large than the time delay imposed by the current references is released in this paper. Moreover, the new synchronization criteria do not impose any restriction on the size of time delay. Numerical examples are finally presented to illustrate the effectiveness of the theoretical results.     

Pinning synchronization of complex network with non-derivative and derivative coupling

This paper investigates synchronization of a complex network with non-derivative and derivative coupling. For achieving the pinning synchronization, the corresponding controllers are designed and applied to only a small fraction of nodes. Both linear and adaptive feedback control methods are used to design controllers. Based on Lyapunov stability theory, several simple and useful criteria for pinning synchronization are derived. Finally, numerical simulations are given to verify the effectiveness of the derived results.     

Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control

This paper investigates the issue of almost sure cluster synchronization in nonlinearly coupled complex networks with nonidentical nodes and time-varying delay. These networks are modulated by a continuous-time Markov chain and disturbed by a Brownian movement. The decentralized adaptive update law and pinning control protocol are employed in designing controllers for guaranteeing almost sure cluster synchronization. By constructing a novel stochastic Lyapunov–Krasovskii function and using the stochastic Lasalle-type invariance theorem, some sufficient conditions for almost sure cluster synchronization of the networks are derived. Finally, a numerical example is given to testify the effectiveness of the theoretical results.     

Adaptive synchronization of T-S fuzzy complex networks with time-varying delays via the pinning control method

In this paper, the synchronization of Takagi–Sugeno (T-S) fuzzy complex networks with time-varying delays and adaptive coupling weights is studied. Using the pinning control and adaptive feedback strategy, a new general class of complex networks with fuzzy logic is proposed and its synchronization is investigated in terms of linear matrix inequalities (LMIs). The adaptive update law of coupling weight is only related to the dynamical behaviors of directly connected nodes. Based on the Lyapunov stability theory, it is proven that the synchronization of the addressed network can be achieved under those control strategies. Finally, two numerical examples are given to verify the effectiveness of our theoretical results.     

Pinning synchronization of weighted complex networks with variable delays and adaptive coupling weights

In this paper, the synchronization for time-delayed complex networks with adaptive coupling weights is studied. A pinning strategy and a local adaptive scheme to determine coupling weights and feedback gains are proposed. It is noted that our control strategies only rely on some local information other than the global information of the whole network. Finally, the developed techniques are applied to two complex networks which are respectively synchronized to an unstable equilibrium point and a chaotic attractor.     

Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix

In this paper, we investigate the cluster synchronization problem for networks with nonlinearly coupled nonidentical dynamical systems and asymmetrical coupling matrix by using pinning control. We derive sufficient conditions for cluster synchronization for any initial values through a feedback scheme and propose an adaptive feedback algorithm that adjusts the coupling strength. Some numerical examples are then given to illustrate the theoretical results.     

Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems

In drive-response complex-variable systems, projective synchronization with respect to a real number, real matrix, or even real function means that drive-response systems evolve simultaneously along the same or inverse direction in a complex plane. However, in many practical situations, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, this paper investigates projective synchronization in drive-response networks of coupled complex-variable chaotic systems with respect to complex numbers, called complex projective synchronization (CPS). The adaptive feedback control method is adopted first to achieve CPS in a general drive-response network. For a special class of drive-response networks, the CPS is achieved via pinning control. Furthermore, a universal pinning control scheme is proposed via the adaptive coupling strength method, several simple and useful criteria for CPS are obtained, and all results are illustrated by numerical examples.     

Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays

In this paper, the problem of adaptive synchronization is investigated for a class of Cohen–Crossberg neural networks with mixed time delays. Based on a Lyapunov–Krasovskii functional and the invariant principle of function differential equations as well as the adaptive control and linear feedback with update law, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving synchronization of the two coupled networks with mixed time delays. In particular, the mixed time delays in this paper synchronously consist of constant delays, time-varying delays, and distributed delays, which are more general than those discussed in the previous literature. Therefore, the results obtained in this paper comprise and generalize those given in the previous literature. A numerical example and its simulation are provided to show the effectiveness of the theoretical results.     

Pinning adaptive synchronization of complex dynamical network with multi-links

Networks with multi-links are universal in the real world such as communication networks, transport networks, and social networks. It is important for us to investigate the control of complex dynamical network with multi-links. In this paper, both local and global stabilities of dynamical network with multi-links are analyzed by applying adaptive control theory and mathematical tools, and some new criteria are proposed to ensure the pinning synchronization. We find that the number of pinned nodes satisfies an inequality for synchronization. Additionally, we solve the problem of how much the coupling strength we need to achieve network synchronization with one pinned node in the network system with multi-links. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.     

Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization

The primary objective of this paper is to propose a new approach for analyzing pinning stability in a complex dynamical network via impulsive control. A?simple yet generic criterion of impulsive pinning synchronization for such coupled oscillator network is derived analytically. It is shown that a single impulsive controller can always pin a given complex dynamical network to a homogeneous solution. Subsequently, the theoretic result is applied to a small-world (SW) neuronal network comprised of the Hindmarsh?CRose oscillators. It turns out that the firing activities of a single neuron can induce synchronization of the underlying neuronal networks. This conclusion is obviously in consistence with empirical evidence from the biological experiments, which plays a significant role in neural signal encoding and transduction of information processing for neuronal activity. Finally, simulations are provided to demonstrate the practical nature of the theoretical results.     

Lag quasisynchronization of coupled delayed systems with parameter mismatch by periodically intermittent control

This paper further investigates the lag synchronization of coupled delayed systems with parameter mismatch. Different from the most existing results, we formulate the intermittent control system that governs the dynamics of the synchronization error. As a result of parameter mismatch, complete lag synchronization cannot be achieved. In this paper, a lag quasisynchronization scheme is proposed to ensure that coupled systems are in a state of lag synchronization with an error level. We estimate the error bound of lag synchronization by rigorously theoretical analysis. Numerical simulations are presented to verify the theoretical results.     

Synchronized regions of pinned complex networks: spectral analysis

The synchronization problem for a complex dynamical network is investigated in this paper from a spectral analysis approach. It is assumed that only a small portion of the nodes in the network are chosen to be controlled, known as the pinning control scheme. Some new types of synchronized regions for networks with different node dynamics and inner-coupling structures are discovered, especially for the case of the special chaotic node systems with a stable equilibrium point under fully anti-diagonal and partially anti-diagonal couplings. The eigenvalue distributions of the coupling and control matrices for different types of complex networks are obtained. The effects of the network topology, global coupling strength, pinning density, and pinning strength on the network synchronizability are examined through extensive numerical simulations. It is shown that the synchronizability of the pinned network can be effectively improved by increasing the overall coupling strength, pinning density, and pinning strength for some classes of synchronized regions, whereas too large the pinning density and pinning strength will lead to desynchronization for other classes. It is found that small-world networks are not always easier to synchronize than regular rings, and a denser eigenvalue distribution may not always imply better synchronizability.     

Aperiodically intermittent control for synchronization of switched complex networks with unstable modes via matrix $$\varvec{\omega }$$-measure approach

The study, by using aperiodically intermittent pinning control, is to synchronize switched delayed complex networks with unstable subsystems. Matrix \(\omega \)-measure and mode-dependent average dwell time method are used to achieve globally exponential synchronization for such system. By designing the useful switching rule and control scheme, we obtain the novel synchronization criteria, which improve the conventional results. Finally, simulation analysis demonstrates the advantages of proposed innovations.     

Intermittent control on switched networks via {\varvec{\omega }}-matrix measure method

This paper is concerned with global exponential synchronization problem for a class of switched delay networks with interval parameters uncertainty, different from the most existing results, without constructing complex Lyapunov–Krasovskii functions; \(\omega \) -matrix measure method is firstly introduced to switched interval networks, combining Halanay inequality technique, designing proper intermittent and non-intermittent control strategy; some easy-to-verify synchronization criteria are given to ensure the global exponential synchronization of switched interval networks under arbitrary switching rule and for admissible interval uncertainties. Moreover, as an application, the proposed scheme can be applied to chaotic neural networks. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results and show the obtained results via employing \(\omega \) -measure are superior to previous results by using \(1\) -measure.     

On pinning synchronization of general coupled networks

The synchronization in general coupled networks subjected to pinning control is investigated. Some generic stability criteria based on the Lyapunov approach are derived for such general controlled networks, which guarantee that the whole network can be pinned to a synchronization state by placing feedback control on only a small fraction of nodes. A real network of television audience flows across 28 satellite channels in China and a representative BA scale-free network composed of chaotic systems are shown, respectively, for illustration and verification. It is found that pinning stability can be improved via increasing pinning density and/or pinning strength for complete diagonal inner coupling.     

Successive lag synchronization on nonlinear dynamical networks via aperiodically intermittent control

Nonlinear Dynamics - Successive lag synchronization (SLS) for nonlinear dynamical networks is investigated by using aperiodically intermittent control. Different from previous works about the SLS,...     

Synchronization of master–slave Lagrangian systems via intermittent control

In this paper, synchronization of master–slave Lagrangian systems via intermittent control was developed. Based on the intermittent control, some algebraic criteria are derived to make the slave Lagrangian system synchronize to a master one. Different from the most existing results on control problems of Lagrangian systems, the controller proposed here is not continuous-time control input and is not relied on the knowledge of system models. As a direct application, the obtained results are applied to a typical two-link revolute jointed robot (robot manipulator). Subsequently, numerical simulations demonstrate the effectiveness of the criteria and the robustness of the control strategy.