scholarly journals Group Synchronization of Nonlinear Complex Dynamics Networks with Sampled Data

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Man Li ◽  
Bo Liu ◽  
Yuqing Zhu ◽  
Lijun Wang ◽  
Mei Zhou
Keyword(s):  
Complex Networks ◽  
Lyapunov Method ◽  
Complex Dynamics ◽  
Complex Dynamical Networks ◽  
Matrix Inequality ◽  
Sampled Data ◽  
Consensus Protocol ◽  
Synchronous State ◽  
Group Synchronization ◽  
Theoretical Results

Based on a nonlinear consensus protocol, this paper considers the group synchronization of complex dynamical networks with sampled data. Using the Lyapunov method, the group synchronization of the nonlinear complex networks is analyzed. All the nodes in each group can converge to their own synchronous state asymptotically, if the sampled period satisfies some matrix inequality conditions. Furthermore, the theoretical results are verified by some simulations.

scholarly journals Sampled-Data-Based Adaptive Group Synchronization of Second-Order Nonlinear Complex Dynamical Networks with Time-Varying Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Bo Liu ◽  
Jiahui Bai ◽  
Yue Zhao ◽  
Chao Liu ◽  
Xuemin Yan ◽  
...  
Keyword(s):  
Adaptive Strategy ◽  
Second Order ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Sampled Data ◽  
Dynamical Networks ◽  
Coupling Strengths ◽  
Simulation Results ◽  
Group Synchronization ◽  
The Given

This paper studies the adaptive group synchronization of second-order nonlinear complex dynamical networks with sampled-data and time-varying delays by designing a new adaptive strategy to feedback gains and coupling strengths. According to Lyapunov stability properties, it is shown that the agents of subgroups can converge the given synchronous states, respectively, under some conditions on the sampled period. Moreover, some simulation results are given.

scholarly journals Sampled-Data Consensus for Nonlinear Multiagent Dynamical Systems via Reliable Control

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Hongjie Li
Keyword(s):  
Dynamical Systems ◽  
Multiagent System ◽  
Random Network ◽  
System Model ◽  
Linear Matrix ◽  
Sampled Data ◽  
Consensus Protocol ◽  
Analysis Technique ◽  
Theoretical Results ◽  
New Distribution

The paper studies sampled-data consensus for nonlinear multiagent dynamical systems. A distributed linear reliable consensus protocol is designed, where probabilistic actuators with different failure rates and random network-induced delay are considered. Based on the input delay approach, a new distribution-based fault multiagent system model with random delay is proposed. By using the stochastic analysis technique and Kronecker product properties, some consensus conditions are derived in terms of linear matrix inequalities, and the solvability of derived conditions depends on not only the failure rate of the actuator but also on the probability of the delay. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Unfragile Control of Uncertain State-Delay Sampled-Data System

2012 ◽  
Vol 433-440 ◽  
pp. 7499-7504
Author(s):  
Xue Liang Wang
Keyword(s):  
Control Problem ◽  
Robust Stability ◽  
Lyapunov Method ◽  
Data System ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Sampled Data ◽  
State Delay ◽  
Numerical Example

The unfragile control problem of a class of uncertain state-delay sampled system is discussed. Applying Lyapunov method, and combining the properties of matrix inequality, the sufficient condition of robust stability is given, and the unfragile controller is designed. Finally a numerical example illustrates the effectiveness and the availability for the design.

scholarly journals Adaptive Exponential Synchronization of Coupled Complex Networks on General Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Song Liu ◽  
Xianfeng Zhou ◽  
Wei Jiang ◽  
Yizheng Fan
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Weighted Graph ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Exponential Rate ◽  
General Graphs ◽  
Theoretical Results ◽  
Variable Coupling

We investigate the synchronization in complex dynamical networks, where the coupling configuration corresponds to a weighted graph. An adaptive synchronization method on general coupling configuration graphs is given. The networks may synchronize at an arbitrarily given exponential rate by enhancing the updated law of the variable coupling strength and achieve synchronization more quickly by adding edges to original graphs. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results.

Pinning synchronization control of complex networks with partial couplings

2020 ◽  
pp. 095965181989833
Author(s):  
Yanzhou Li ◽  
Yishan Liu ◽  
Yuanqing Wu ◽  
Shenghuang He
Keyword(s):  
Complex Networks ◽  
Linear Matrix ◽  
Sampled Data ◽  
Lower And Upper Bounds ◽  
Target Node ◽  
Decoupling Method ◽  
Synchronization Problem ◽  
Sampling Intervals ◽  
Wirtinger’S Inequality ◽  
Theoretical Results

In this article, the pinning synchronization problem of complex networks with a target node via sampled-data communications is considered. Due to partial couplings among the nodes in complex networks, a decoupling method is adopted to investigate each channel of complex networks independently. By constructing a time-dependent Lyapunov function, it is proved that the pinning synchronization of complex networks with a target node can be achieved if the control parameters are appropriately selected. Furthermore, further study is needed to investigate the pinning synchronization of complex networks in the presence of constant delay. A novel criterion is obtained using Jensen’s inequality and Wirtinger’s inequality. It is worth noting that the lower and upper bounds of the sampling intervals can be calculated by linear matrix inequality box of MATLAB. Theoretical results are well verified through a numerical simulation.

scholarly journals Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 405 ◽  
Author(s):  
Xudong Hai ◽  
Guojian Ren ◽  
Yongguang Yu ◽  
Conghui Xu
Keyword(s):  
Complex Networks ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Communication Topology ◽  
General Network ◽  
Inequality Techniques ◽  
Adaptive Control Strategy ◽  
Pinning Scheme

In this paper, a class of fractional complex networks with impulses and reaction–diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results.

Cluster Mixed Synchronization of Complex Networks with Disturbance

2015 ◽  
Vol 719-720 ◽  
pp. 448-451
Author(s):  
Li Jie Zeng
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Bounded Disturbances ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, we investigate the cluster mixed synchronization scheme in time-varying delays coupled complex dynamical networks with disturbance. Basing on the community structure of the networks, some sufficient criteria are derived to ensure cluster mixed synchronization of the network model. Particularly, unknown bounded disturbances can be conquered by the proposed control. The numerical simulations are performed to verify the effectiveness of the theoretical results

scholarly journals Adaptive Synchronization of Complex Dynamical Networks with State Predictor

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yuntao Shi ◽  
Bo Liu ◽  
Xiao Han
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulations ◽  
Lyapunov Method ◽  
Adaptive Strategy ◽  
Convergence Speed ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Dynamical Networks ◽  
Synchronous State ◽  
Coupling Strengths

This paper addresses the adaptive synchronization of complex dynamical networks with nonlinear dynamics. Based on the Lyapunov method, it is shown that the network can synchronize to the synchronous state by introducing local adaptive strategy to the coupling strengths. Moreover, it is also proved that the convergence speed of complex dynamical networks can be increased via designing a state predictor. Finally, some numerical simulations are worked out to illustrate the analytical results.

CHAOS GENERATION FOR A CLASS OF NONLINEAR COMPLEX NETWORKS

2013 ◽  
Vol 23 (02) ◽  
pp. 1350018 ◽  
Author(s):  
NA LIU ◽  
JUAN LI ◽  
ZHI-HONG GUAN ◽  
LI DING ◽  
GUILIN ZHENG
Keyword(s):  
Lyapunov Exponent ◽  
Complex Networks ◽  
Mathematical Analysis ◽  
Research Topic ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Numerical Example ◽  
Emergence Of Chaos ◽  
New Criteria ◽  
Theoretical Results

Chaos generation is an interesting research topic in the study of coupled complex dynamical networks. In this paper, based on mathematical analysis of Lyapunov exponent and boundedness of networks, the emergence of chaos for a class of nonlinear complex networks is investigated and some new criteria of chaos generation are derived. The effectiveness of theoretical results is verified by a numerical example.

Dynamical Behaviors of Stochastic Hopfield Neural Networks with Reaction-Diffusion Terms

2013 ◽  
Vol 432 ◽  
pp. 523-527
Author(s):  
Qing Hua Zhou ◽  
Li Wan
Keyword(s):  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Hopfield Neural Network ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ultimate Boundedness ◽  
Dynamical Behaviors ◽  
Diffusion Effects ◽  
Weak Attractor ◽  
Theoretical Results

Dynamical behaviors of stochastic Hopfield neural network with delays and reaction-diffusion terms are investigated. By employing Lyapunov method, Poincare inequality and linear matrix inequality, some novel criteria on ultimate boundedness, weak attractor and asymptotic stability are obtained. The criteria are independent of the magnitude of the delays, and dependent on the diffusion effects and the derivative of the delays. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

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