Adaptive impulsive cluster synchronization in community network with nonidentical nodes

2016 ◽  
Vol 27 (01) ◽  
pp. 1650010 ◽  
Author(s):  
Xiaoli Gong ◽  
Luyining Gan ◽  
Zhaoyan Wu
Keyword(s):  
Impulsive Control ◽  
Adaptive Strategy ◽  
Cluster Synchronization ◽  
Community Network ◽  
Analysis Technique ◽  
Control Scheme ◽  
Lyapunov Function Method ◽  
Nonidentical Nodes ◽  
Proper Values ◽  
Theoretical Results

In this paper, cluster synchronization in community network with nonidentical nodes is investigated. Through introducing proper adaptive strategy into impulsive control scheme, adaptive impulsive controllers are designed for achieving the cluster synchronization. In this adaptive impulsive control scheme, for any given networks, the impulsive gains can adjust themselves to proper values according to the proposed adaptive strategy when the impulsive intervals are fixed. The impulsive instants can be estimated by solving a sequence of maximum value problems when the impulsive gains are fixed. Both community networks without and with coupling delay are considered. Based on the Lyapunov function method and mathematical analysis technique, two synchronization criteria are derived. Several numerical examples are performed to verify the effectiveness of the derived theoretical results.

Exponential synchronization in complex-variable network with distributed delays via intermittent control

2017 ◽  
Vol 28 (07) ◽  
pp. 1750089 ◽  
Author(s):  
Sulan He ◽  
Guisheng Yi ◽  
Zhaoyan Wu
Keyword(s):  
Complex Variable ◽  
Exponential Synchronization ◽  
Distributed Delays ◽  
Intermittent Control ◽  
Control Gain ◽  
Analysis Technique ◽  
Control Scheme ◽  
Lyapunov Function Method ◽  
And Control ◽  
Theoretical Results

In this paper, exponential synchronization in complex-variable network with distributed delays is investigated. By utilizing intermittent control scheme, some effective controllers are designed. Based on the Lyapunov function method and mathematical analysis technique, some synchronization criteria with respect to the system parameters, control gain and control rate are presented. From the criteria, for any given dynamical network, the needed values of control gains and rate can be easily estimated. Finally, two numerical simulations are performed to verify the derived theoretical results.

scholarly journals Cluster Synchronization for Linearly Coupled Complex Networks with Identical and Nonidentical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Adaptive Feedback ◽  
Numerical Examples ◽  
Control Schemes ◽  
Nonidentical Nodes ◽  
Theoretical Results

The cluster synchronization of linearly coupled complex networks with identical and nonidentical nodes is studied. Without assuming symmetry, we proved that these linearly coupled complex networks could achieve cluster synchronization under certain pinning control schemes. Sufficient conditions guaranteeing cluster synchronization for any initial values are derived by using Lyapunov function methods. Moreover, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical examples are given to illustrate our theoretical results.

scholarly journals Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy

2021 ◽  
Vol 26 (6) ◽  
pp. 993-1011
Author(s):  
Mei Liu ◽  
Jie Chen ◽  
Haijun Jiang ◽  
Zhiyong Yu ◽  
Cheng Hu ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Adaptive Strategy ◽  
Auxiliary Function ◽  
Intermittent Control ◽  
Global Synchronization ◽  
Delayed Systems ◽  
Control Gain ◽  
Analysis Technique ◽  
Theoretical Results

In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme.

scholarly journals Hub-Induced Synchronization in Scale-Free Networks with Cluster Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianbao Zhang ◽  
Zhongjun Ma ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Cluster Structure ◽  
Sufficient Conditions ◽  
Cluster Synchronization ◽  
Numerical Examples ◽  
Scale Free ◽  
Lyapunov Function Method ◽  
Scale Free Networks ◽  
Theoretical Results

A recent research indicated that the corticocortical connectivity network of the cat possesses cluster structure and that each cluster in the network is scale-free and has a most connected hub. Motivated by that research, we slightly modify the network model and derive sufficient conditions for cluster synchronization of the modified network based on Lyapunov function method. The obtained results indicate that cluster synchronization can be induced by the hubs of the scale-free networks. In our opinion, the concept of hub-induced synchronization provides a better understanding of cluster synchronization in scale-free networks. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

scholarly journals Finite-Time Adaptive Fuzzy Control for Nonlinear Systems with Unknown Backlash-Like Hysteresis

2021 ◽  
Author(s):  
Shuzhen Diao ◽  
Wei Sun ◽  
Le Wang ◽  
Jing Wu
Keyword(s):  
Fuzzy Control ◽  
Finite Time ◽  
Fuzzy Systems ◽  
Tracking Error ◽  
Adaptive Fuzzy Control ◽  
Finite Time Stability ◽  
Adaptive Fuzzy ◽  
Intermediate Variable ◽  
Control Scheme ◽  
Theoretical Results

AbstractThis study considers the tracking control problem of the nonstrict-feedback nonlinear system with unknown backlash-like hysteresis, and a finite-time adaptive fuzzy control scheme is developed to address this problem. More precisely, the fuzzy systems are employed to approximate the unknown nonlinearities, and the design difficulties caused by the nonlower triangular structure are also overcome by using the property of fuzzy systems. Besides, the effect of unknown hysteresis input is compensated by approximating an intermediate variable. With the aid of finite-time stability theory, the proposed control algorithm could guarantee that the tracking error converges to a smaller region. Finally, a simulation example is provided to further verify the above theoretical results.

scholarly journals Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramziya Rifhat ◽  
Zhidong Teng ◽  
Chunxia Wang
Keyword(s):  
Epidemic Model ◽  
Control Strategies ◽  
Random Perturbations ◽  
Disease Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Analysis Theory ◽  
Lyapunov Function Method ◽  
Random Fluctuations ◽  
Theoretical Results

AbstractIn this paper, a stochastic SIRV epidemic model with general nonlinear incidence and vaccination is investigated. The value of our study lies in two aspects. Mathematically, with the help of Lyapunov function method and stochastic analysis theory, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics. In other words, neglecting random perturbations overestimates the ability of the disease to spread. The numerical simulations are given to illustrate the main theoretical results.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

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