scholarly journals Exponential Synchronization of Stochastic Complex Dynamical Networks with Impulsive Perturbations and Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Wuneng Zhou ◽  
Anding Dai ◽  
Dongbing Tong ◽  
Jun Yang
Keyword(s):  
Stochastic Analysis ◽  
Function Method ◽  
Transition Probability ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Markovian Switching ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
Lyapunov Function Method

This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbation and Markovian switching. The complex dynamical networks consist ofκmodes, and the networks switch from one mode to another according to a Markovian chain with known transition probability. Based on the Lyapunov function method and stochastic analysis, by employingM-matrix approach, some sufficient conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbation and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, two numerical examples are included to show the effectiveness of our results.

scholarly journals Pinning Synchronization of Switched Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liming Du ◽  
Feng Qiao ◽  
Fengying Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Function Method ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Dynamical Networks ◽  
Switching Law ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
Networks With Switching Topology

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

scholarly journals Neural network based asynchronous synchronization for fuzzy hidden Markov jump complex dynamical networks

2021 ◽  
Author(s):  
Chao Ma ◽  
Liziyi Hao ◽  
Hang Fu
Keyword(s):  
Neural Network ◽  
Hidden Markov ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Markov Jump ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
The Neural Network ◽  
Takagi Sugeno

AbstractThis paper investigates the drive-response synchronization problem of Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks. More precisely, a novel asynchronous synchronization control strategy is developed for coping with mismatched hidden jumping modes. Furthermore, the neural network is adopted with online learning laws for unknown function approximation. By taking advantage of Lyapunov method, sufficient conditions are established to ensure mean-square synchronization performance with disturbances. Based on the synchronization criterion, asynchronous controller gains are designed in terms of linear matrix inequalities. An illustrative example is finally given to validate the effectiveness of the proposed synchronization techniques.

scholarly journals Mean-Square Exponential Synchronization of Stochastic Complex Dynamical Networks with Switching Topology by Impulsive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xuefei Wu ◽  
Chen Xu
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Linear Matrix ◽  
Mean Square ◽  
Dynamical Networks ◽  
The Mean ◽  
Networks With Switching Topology

This paper investigates the mean-square exponential synchronization issues of delayed stochastic complex dynamical networks with switching topology and impulsive control. By using the Lyapunov functional method, impulsive control theory, and linear matrix inequality (LMI) approaches, some sufficient conditions are derived to guarantee the mean-square exponential synchronization of delay complex dynamical network with switch topology, which are independent of the network size and switch topology. Numerical simulations are given to illustrate the effectiveness of the obtained results in the end.

FINITE-TIME SYNCHRONIZATION OF DYNAMICAL NETWORKS COUPLED WITH COMPLEX-VARIABLE CHAOTIC SYSTEMS

2013 ◽  
Vol 24 (09) ◽  
pp. 1350058 ◽  
Author(s):  
ZHAOYAN WU ◽  
QINGLING YE ◽  
DANFENG LIU
Keyword(s):  
Complex Variable ◽  
Finite Time ◽  
Function Method ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Dynamical Networks ◽  
Finite Time Stability ◽  
Lyapunov Function Method

In this paper, finite-time synchronization of dynamical networks coupled with complex-variable chaotic systems is investigated. According to Lyapunov function method and finite-time stability theory, both the dynamical networks without and with coupling delay are considered through designing proper finite-time controllers. Several sufficient conditions for finite-time synchronization are derived and verified to be effective by some numerical examples.

scholarly journals Pinning Adaptive Synchronization of Delayed Coupled Dynamical Networks via Periodically Intermittent Control

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Xueliang Liu ◽  
Shengbing Xu
Keyword(s):  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Adaptive Synchronization ◽  
Intermittent Control ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Periodically Intermittent Control ◽  
Synchronization Problem ◽  
Theoretical Results

This paper investigates the exponential synchronization problem of delayed coupled dynamical networks by using adaptive pinning periodically intermittent control. Based on the Lyapunov method, by designing adaptive feedback controller, some sufficient conditions are presented to ensure the exponential synchronization of coupled dynamical networks with delayed coupling. Furthermore, a numerical example is given to demonstrate the validity of the theoretical results.

scholarly journals Adaptive Impulsive Observer for Outer Synchronization of Delayed Complex Dynamical Networks with Output Coupling

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Song Zheng
Keyword(s):  
Control Method ◽  
Hybrid Control ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Output Coupling ◽  
Lyapunov Stability Theorem ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
Control Schemes ◽  
Theoretical Results

The synchronization problem of two delayed complex dynamical networks with output coupling is investigated by using impulsive hybrid control schemes, where only scalar signals need to be transmitted from the drive network to the response one. Based on the Lyapunov stability theorem and the impulsive hybrid control method, some sufficient conditions guaranteeing synchronization of such complex networks are established for both the cases of coupling delay and node delay are considered, respectively. Finally, two illustrative examples with numerical simulations are given to show the feasibility and efficiency of theoretical results.

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