scholarly journals Synchronization Analysis of Two Coupled Complex Networks with Time Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Weigang Sun ◽  
Jingyuan Zhang ◽  
Changpin Li
Keyword(s):  
Theoretical Analysis ◽  
Complex Networks ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Time Delays ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Numerical Examples ◽  
Outer Synchronization ◽  
Matrix Equality

This paper studies the synchronized motions between two complex networks with time delays, which include individual inner synchronization in each network and outer synchronization between two networks. Based on the Lyapunov stability theory and the linear matrix equality (LMI), a synchronous criterion for inner synchronization inside each network is derived. Numerical examples are given which fit the theoretical analysis. In addition, the involved numerical results show that the delays between two networks have little effect on inner synchronization. It is also shown that synchronous motions within each network or between two networks are not enhanced if individual intranetwork connections are allowed.

ROBUST H∞ FILTERING FOR A CLASS OF NONLINEAR UNCERTAIN SINGULAR SYSTEMS WITH TIME-VARYING DELAY

2013 ◽  
Vol 11 (05) ◽  
pp. 1350035 ◽  
Author(s):  
JIQING QIU ◽  
ZIRUI XING ◽  
LI LI ◽  
MOHAN YANG ◽  
YI LI
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Singular Systems ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Satisfy Lipschitz Condition ◽  
Uncertain Singular Systems ◽  
Varying Delay

This paper focuses on the problem of robust H∞ filtering for a class of nonlinear uncertain singular systems with time-varying delay. First of all, the definition of robust H∞ filter is given. Considering the nonlinear disturbance link to uncertain singular systems with time-varying delay effects, the design idea of full-order robust H∞ filter based on the Lyapunov stability theory is presented. Under the condition that nonlinear uncertain functions satisfy Lipschitz condition, the sufficient condition under which nonlinear uncertain delayed filtering error singular systems are asymptotically stable and satisfy the robust H∞ performance is obtained by Lyapunov stability theory and linear matrix inequality (LMI) methods. Finally, two numerical examples are given to show the applicability of the proposed method.

Active Anti-Synchronization Between Identical and Distinctive Hyperchaotic Systems

2008 ◽  
Vol 15 (04) ◽  
pp. 371-382 ◽  
Author(s):  
M. M. Al-sawalha ◽  
M. S. M. Noorani
Keyword(s):  
Theoretical Analysis ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
High Dimensional ◽  
Analysis Strategy ◽  
Relevant Variables ◽  
Hyperchaotic Systems

This paper brings attention to hyperchaos anti-synchronization between two identical and distinctive hyperchaotic systems using active control theory. The sufficient conditions for achieving anti-synchronization of two high dimensional hyperchaotic systems is derived based on Lyapunov stability theory, where the controllers are designed by using the sum of relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

scholarly journals Outer Synchronization of a Modified Quorum-Sensing Network via Adaptive Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jianbao Zhang ◽  
Wenyin Zhang ◽  
Denghua Zhang ◽  
Chengdong Yang ◽  
Kongwei Zhu ◽  
...  
Keyword(s):  
Adaptive Control ◽  
Quorum Sensing ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Negative Effects ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Outer Synchronization ◽  
Noise Disturbances

Motivated by the quorum-sensing mechanism of bacteria, this paper modifies the network model by adding unknown parameters and noise disturbances and investigates the problem of outer synchronization via adaptive control. In case there exist three unknown parameters, updating laws are presented to identify the unknown parameters with help of Lyapunov stability theory, and the negative effects of noise disturbances are also compensated by designing adaptive controllers. In addition, we simplify the obtained conditions and carry out two succinct and utilitarian corollaries. Finally, numerical simulations are provided to show the validity of the obtained results.

scholarly journals Navigational Protocols of Formation Control for Multiagent Network with and without Nonlinear Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Shaolin Li ◽  
Yinghui He ◽  
Lili Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Control Problem ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Formation Control ◽  
Lyapunov Stability Theory ◽  
Numerical Examples ◽  
Current Location ◽  
Multiagent Networks ◽  
The Difference

Formation control problem for multiagent networks is investigated under the framework of leader-follower consensus. By utilizing the Lyapunov stability theory, two navigational protocols for multiagent network without and with nonlinear dynamics are derived to realize formation control, respectively. In order to achieve the expected formation, controller is adopted to each agent, and the design philosophies of control protocol are required to follow two rules: (i) the destinations of agent are required to be identified and communicating with each other through the network; (ii) at least one agent is needed to be navigator which can detect the difference between its current location and destination. Finally, the two numerical examples are provided to demonstrate the effectiveness of the proposed navigational protocols.

scholarly journals Lag Synchronization of Hyperchaotic Systems via Intermittent Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Junjian Huang ◽  
Chuandong Li ◽  
Wei Zhang ◽  
Pengcheng Wei ◽  
Qi Han
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Intermittent Control ◽  
Lag Synchronization ◽  
Control Scheme ◽  
Hyperchaotic Systems ◽  
Theoretical Results

Different from the most existing results, in this paper an intermittent control scheme is designed to achieve lag synchronization of coupled hyperchaotic systems. Several sufficient conditions ensuring lag synchronization are proposed by rigorous theoretical analysis with the help of the Lyapunov stability theory. Numerical simulations are also presented to show the effectiveness and feasibility of the theoretical results.

scholarly journals Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Xiaomei Cai
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Combination Synchronization ◽  
Special Cases ◽  
Complex Chaotic Systems

This paper investigates the combination-combination synchronization of four nonlinear complex chaotic systems. Based on the Lyapunov stability theory, corresponding controllers to achieve combination-combination synchronization among four different nonlinear complex chaotic systems are derived. The special cases, such as combination synchronization and projective synchronization, are studied as well. Numerical simulations are given to illustrate the theoretical analysis.

scholarly journals Anti-Synchronization of Fractional-Order Chaotic Circuit with Memristor via Periodic Intermittent Control

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Intermittent Control ◽  
Chaotic Circuit ◽  
Control Scheme

In this paper, the anti-synchronization of fractional-order chaotic circuit with memristor (FCCM) is investigated via a periodic intermittent control scheme. Based on the principle of periodic intermittent control and the Lyapunov stability theory, a novel criterion is adopted to realize the anti-synchronization of FCCM. Finally, some examples of numerical simulations are exploited to verify the feasibility of theoretical analysis.

Chaos Synchronization Modle of Complex Networks on Real Estate Investment Systems

2014 ◽  
Vol 501-504 ◽  
pp. 2715-2718
Author(s):  
Hua Li
Keyword(s):  
Real Estate ◽  
Complex Networks ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Drive System ◽  
Real Estate Investment ◽  
Response System

This paper gives the complex networks chaos modle on real estate investment systems and brings attention to Chaos synchronizati -on between real estate investment drive system and economic increase response system .The sufficient conditions for achieving the synchroni -zation of two systems are derived based on Lyapunov stability theory .

scholarly journals Synchronization between Two Discrete-Time Networks with Mutual Couplings

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Meng Xiao ◽  
Weigang Sun ◽  
Fangyue Chen
Keyword(s):  
Theoretical Analysis ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Numerical Examples ◽  
Outer Synchronization ◽  
Topological Structures ◽  
Coupling Strengths

We investigate synchronization between two discrete-time networks with mutual couplings, including inner synchronization inside each network and outer synchronization between two networks. We then obtain a synchronized criterion for the inner synchronization inside each network by the method of linear matrix inequality and derive a relationship between the inner and outer synchronization. Finally, we show numerical examples to verify our theoretical analysis and discuss the effect of coupling strengths, node dynamics, and topological structures on the inner and outer synchronization. Compared to the inner synchronization inside each network, the outer synchronization between two networks is difficult to achieve.

scholarly journals Adaptive Anti-synchronization of Identical and Non-identical 4-D Chaotic Systems

2012 ◽  
pp. 160-164
Author(s):  
H. Najafizadegan ◽  
M. Khoeiniha ◽  
H. Zarabadipour
Keyword(s):  
Adaptive Control ◽  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Unknown Parameters ◽  
Different Chaotic Systems ◽  
Adaptive Control Law

In this paper, we investigate the chaos anti-synchronization between two identical and different chaotic systems with fully unknown parameters via adaptive control. Based on the Lyapunov stability theory, an adaptive control law and a parameter update rule for unknown parameters are designed such that the two different chaotic systems can be anti-synchronized asymptotically. Theoretical analysis and numerical simulations are shown to verify the results.

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