scholarly journals Passivity Analysis of Complex Delayed Dynamical Networks with Output Coupling

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yan-Fang Kang ◽  
Lu-Xian Fang ◽  
Yue-Hui Zhao ◽  
Shun-Yan Ren
Keyword(s):  
Network Model ◽  
Sufficient Conditions ◽  
Output Coupling ◽  
Lyapunov Functionals ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
Dynamical Network ◽  
Passivity Analysis ◽  
Delayed Dynamical Networks

A new complex dynamical network model with output coupling is proposed. This paper is concerned with input passivity and output passivity of the proposed network model. By constructing new Lyapunov functionals, some sufficient conditions ensuring the input passivity and output passivity are obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed results.

scholarly journals A New Model for Complex Dynamical Networks Considering Random Data Loss

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 797
Author(s):  
Xu Wu ◽  
Guo-Ping Jiang ◽  
Xinwei Wang
Keyword(s):  
Network Model ◽  
Network Models ◽  
Lyapunov Stability Theory ◽  
Complex Dynamical Networks ◽  
Output Coupling ◽  
Data Loss ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Dynamical Network ◽  
Proposed Model

Model construction is a very fundamental and important issue in the field of complex dynamical networks. With the state-coupling complex dynamical network model proposed, many kinds of complex dynamical network models were introduced by considering various practical situations. In this paper, aiming at the data loss which may take place in the communication between any pair of directly connected nodes in a complex dynamical network, we propose a new discrete-time complex dynamical network model by constructing an auxiliary observer and choosing the observer states to compensate for the lost states in the coupling term. By employing Lyapunov stability theory and stochastic analysis, a sufficient condition is derived to guarantee the compensation values finally equal to the lost values, namely, the influence of data loss is finally eliminated in the proposed model. Moreover, we generalize the modeling method to output-coupling complex dynamical networks. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed model.

scholarly journals Effects of Time-Varying Impulses on the Synchronization of Delayed Dynamical Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shuiming Cai ◽  
Peipei Zhou ◽  
Zengrong Liu
Keyword(s):  
Network Model ◽  
Comparison Principle ◽  
Network Topology ◽  
Spanning Tree ◽  
Time Varying ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
General Complex ◽  
Delayed Dynamical Networks ◽  
Theoretical Results

The effects of time-varying impulses on the synchronization of a class of general complex delayed dynamical networks are investigated. Different from the existing works, the impulses discussed here are time-varying, and both synchronizing and desynchronizing impulses are considered in the network model simultaneously. Moreover, the network topology is assumed to be directed and weakly connected with a spanning tree. By using the comparison principle, some simple yet generic globally exponential synchronization criteria are derived. It is shown that besides impulse strengths and impulsive interval, the obtained criteria are also closely related with topology structure of the network. Finally, numerical examples are given to demonstrate the effectiveness of the theoretical results.

EFFECTS OF COUPLING DELAYS ON SYNCHRONIZATION IN LUR'E COMPLEX DYNAMICAL NETWORKS

2010 ◽  
Vol 20 (11) ◽  
pp. 3565-3584 ◽  
Author(s):  
KE DING ◽  
QING-LONG HAN
Keyword(s):  
Complex Dynamical Networks ◽  
Lyapunov Functionals ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Decomposition Approach ◽  
Lur’E System ◽  
Numerical Example ◽  
Dynamical Network ◽  
Delay Decomposition Approach ◽  
Delay Decomposition

This paper investigates the effects of coupling delays on synchronization in Lur'e complex dynamical networks. Every identical node in the network can be represented as a Lur'e system. Based on Lyapunov–Krasovskii functionals and Lur'e–Postnikov Lyapunov functionals, some delay-dependant synchronization criteria are derived by employing a delay decomposition approach. A Lur'e complex dynamical network with Chua's circuit nodes and one numerical example are given to illustrate the effectiveness of the synchronization criteria.

scholarly journals Synchronization in a Novel Local-World Dynamical Network Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jianeng Tang ◽  
Peizhong Liu
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Network Model ◽  
Optimal Growth ◽  
Dynamical Networks ◽  
Dynamical Network ◽  
Network Research ◽  
Topology Model ◽  
The Relationship ◽  
Random Failures

Advances in complex network research have recently stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. In the paper, we study the synchronizability of a class of local-world dynamical networks. Then, we have proposed a local-world synchronization-optimal growth topology model. Compared with the local-world evolving network model, it exhibits a stronger synchronizability. We also investigate the robustness of the synchronizability with respect to random failures and the fragility of the synchronizability with specific removal of nodes.

scholarly journals Input and Output Passivity of Complex Dynamical Networks with General Topology

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Jinliang Wang
Keyword(s):  
Linear Matrix Inequalities ◽  
General Topology ◽  
Linear Matrix ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Dynamical Network ◽  
Dynamical Network ◽  
Input And Output ◽  
Generalized Complex

The input passivity and output passivity are investigated for a generalized complex dynamical network, in which the coupling may be nonlinear, time-varying, and nonsymmetric. By constructing some suitable Lyapunov functionals, some input and output passivity criteria are derived in form of linear matrix inequalities (LMIs) for complex dynamical network. Finally, a numerical example and its simulation are given to illustrate the efficiency of the derived results.

scholarly journals Topology Detection for Output-Coupling Weighted Complex Dynamical Networks with Coupling and Transmission Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Xinwei Wang ◽  
Guo-Ping Jiang ◽  
Chunxia Fan ◽  
Xu Wu
Keyword(s):  
Dynamical System ◽  
Numerical Simulations ◽  
Invariance Principle ◽  
Time Delays ◽  
Complex Dynamical Networks ◽  
Output Coupling ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Transmission Delays ◽  
Response System

Topology detection for output-coupling weighted complex dynamical networks with two types of time delays is investigated in this paper. Different from existing literatures, coupling delay and transmission delay are simultaneously taken into account in the output-coupling network. Based on the idea of the state observer, we build the drive-response system and apply LaSalle’s invariance principle to the error dynamical system of the drive-response system. Several convergent criteria are deduced in the form of algebraic inequalities. Some numerical simulations for the complex dynamical network, with node dynamics being chaotic, are given to verify the effectiveness of the proposed scheme.

scholarly journals Pinning Cluster Synchronization in Linear Hybrid Coupled Delayed Dynamical Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-14
Author(s):  
Anping Bao ◽  
Ting Wang ◽  
Shumin Fei ◽  
Xiaomin Tian
Keyword(s):  
Control Strategy ◽  
Kronecker Product ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Dynamical Networks ◽  
Delayed Dynamical Networks

The problem on cluster synchronization will be investigated for a class of delayed dynamical networks based on pinning control strategy. Through utilizing the combined convex technique and Kronecker product, two sufficient conditions can be derived to ensure the desired synchronization when the designed feedback controller is employed to each cluster. Moreover, the inner coupling matrices are unnecessarily restricted to be diagonal and the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which greatly improve the present methods. Finally, two numerical examples are provided to demonstrate the effectiveness and reduced conservatism.

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