Nonlinearly Coupled Complex Dynamical Networks Research Articles

Pinning clustering component synchronization of nonlinearly coupled complex dynamical networks

<abstract><p>In this paper, the clustering component synchronization of nonlinearly coupled complex dynamical networks with nonidentical nodes was investigated. By applying feedback injections to those nodes who have connections with other clusters, some criteria for achieving clustering component synchronization were obtained. A numerical simulation was also included to verify the correctness of the results obtained.</p></abstract>

Adaptive Synchronization of Complex Dynamical Networks via Distributed Pinning Impulsive Control

In this paper, exponential synchronization of a class of nonlinearly coupled complex dynamical networks with time-varying delay is investigated. A novel distributed controller combined with pinning impulsive method is designed by selecting the systems with largest norms of errors to be controlled at every impulsive instant. By introducing the adaptive control protocol into the negative feedback controller, suitable control gains are obtained and therefore, the control cost is efficiently saved. Based on the Lyapunov stability theory and some mathematical techniques, some novel leader-following synchronization criteria are derived. Furthermore, with consideration of time-varying impulsive effects, the obtained results are extended to a more complicated situation. Finally, two numerical examples are performed to illustrate the effectiveness of the theoretical analysis.

Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

Global Exponential Synchronization of Nonlinearly Coupled Complex Dynamical Networks with Time-Varying Coupling Delays

This paper focuses on the global exponential synchronization problem of nonlinearly coupled complex dynamical networks with time-varying coupling delays. Several simple and generic global exponential synchronization criteria are derived based on the Lyapunov stability theory and the Dini derivatives using the Halanay and generalized Halanay inequalities. These criteria rely on system parameters alone and can be used conveniently in practical applications. In addition, the system parameters do not satisfy the conditions of the proposed criteria. That is, the system itself cannot synchronize. However, system synchronization can be achieved by adding the appropriate feedback controllers, thereby providing a practical and effective control method for complex dynamical networks. An estimation method of exponential convergence rate is also presented. Finally, the effectiveness of the proposed criteria is verified through numerical simulations.

Global synchronization of nonlinear coupled complex dynamical networks with information exchanges at discrete-time

This paper studies the problem of synchronization for a class of complex networks with discrete-time couplings. The intrinsic local dynamical behaviors of the nodes in the complex networks are varied continuously while the manners of information interaction between every two different nodes are discrete time-varying rather than proceeded continuously, that is, the communications of the nodes only active at some discrete instants. Similar to the sampled data control systems, we convert the discrete time coupling issue into an effective time-varying delayed coupling network. By constructing the Lyapunov function skillfully, sufficient conditions are derived to guarantee the realization of the synchronization pattern for all initial values based on the Lyapunov stability theorem and linear matrix inequalities. What is more, the maximum allowable sampling period for communication is obtained through a optimization problem. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

Synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers

This paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers. We propose a dynamical network mathematical model with similar nonlinear nodes, whose dimensions are different. For this kind of network model, the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes. In addition, the synchronisation manifold is defined as an invariant manifold, which is regarded as the generalised case of dynamical networks with the same nodes’ dynamics. Furthermore, some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis. Finally, numerical examples are presented to verify the effectiveness of the obtained theoretical results.

Topology identification of uncertain nonlinearly coupled complex networks with delays based on anticipatory synchronization

This paper presents an adaptive anticipatory synchronization based method for simultaneous identification of topology and parameters of uncertain nonlinearly coupled complex dynamical networks with time delays. An adaptive controller is proposed, based on Lyapunov stability theorem and Barbǎlat's Lemma, to guarantee the stability of the anticipatory synchronization manifold between drive and response networks. Meanwhile, not only the identification criteria of network topology and system parameters are obtained but also the anticipatory time is identified. Numerical simulation results illustrate the effectiveness of the proposed method.

Cluster Synchronization of Time‐Varying Delays Coupled Complex Networkswith Nonidentical Dynamical Nodes

This paper investigates a new cluster synchronization scheme in the nonlinear coupled complex dynamical networks with nonidentical nodes. The controllers are designed based on the community structure of the networks; some sufficient criteria are derived to ensure cluster synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be symmetric, irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.

Adaptive synchronization of two nonlinearly coupled complex dynamical networks with delayed coupling

This paper investigates the adaptive synchronization between two nonlinearly delay-coupled complex networks with the bidirectional actions and nonidentical topological structures. Based on LaSalle’s invariance principle, some criteria for the synchronization between two coupled complex networks are achieved via adaptive control. To validate the proposed methods, the unified chaotic system as the nodes of the networks are analyzed in detail, and numerical simulations are given to illustrate the theoretical results.