Cluster modified projective synchronization between community networks

2015 ◽  
Vol 26 (10) ◽  
pp. 1550110 ◽  
Author(s):  
Shahed Vahedi ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Adaptive Control ◽  
Controller Design ◽  
Lyapunov Stability Theory ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Community Networks ◽  
Arbitrary Matrix ◽  
Control Gain ◽  
Modified Projective Synchronization ◽  
Matrix Scaling

Cluster modified projective synchronization of two community networks with nonidentical nodes is studied in this paper. Each network has a unique dynamics and its clusters have different parameter sets which could make their dynamics chaotic or periodic for instance. Therefore, we are dealing with varieties of dynamics in these clusters. By introducing an adaptive control gain in our controller design and using Lyapunov stability theory, we show that two community networks can reach to the synchronized state having arbitrary matrix scaling factor between corresponding nodes of the networks. Moreover, using this matrix we can observe different synchronization regimes simultaneously in each pair of corresponding nodes.

Cluster modified projective synchronization between networks with distinct topologies

2016 ◽  
Vol 27 (08) ◽  
pp. 1650087 ◽  
Author(s):  
Shahed Vahedi ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Lyapunov Stability Theory ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Community Networks ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Control Gain ◽  
Modified Projective Synchronization ◽  
Hybrid Synchronization ◽  
Matrix Scaling

Cluster modified projective synchronization (CMPS) between two topologically distinct community networks is studied in this paper. Each cluster here has a unique dynamics at least with respect to the parameter sets. Using an adaptive feedback control gain and a matrix scaling factor, we show that CMPS between two community networks can be realized with considering minimum assumptions and imposing just few restrictions on the configuration set. We use Lyapunov stability theory for the proof and employ computer simulation to confirm our result on randomly generated community networks. Simulations also show the possibility of having hybrid synchronization between the two networks.

scholarly journals Robust Controller Design for Modified Projective Synchronization of Chen-Lee Chaotic Systems with Nonlinear Inputs

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Jui-sheng Lin ◽  
Neng-Sheng Pai ◽  
Her-Terng Yau
Keyword(s):  
Chaotic Systems ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Variable Structure ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Nonlinear Controller ◽  
Input Nonlinearity ◽  
Structure Control ◽  
Modified Projective Synchronization

This study demonstrates the modified projective synchronization in Chen-Lee chaotic system. The variable structure control technology is used to design the synchronization controller with input nonlinearity. Based on Lyapunov stability theory, a nonlinear controller and some generic sufficient conditions can be obtained to guarantee the modified projective synchronization, including synchronization, antisynchronization, and projective synchronization in spite of the input nonlinearity. The numerical simulation results show that the synchronization and antisynchronization can coexist in Chen-Lee chaotic systems. It demonstrates the validity and feasibility of the proposed controller.

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

scholarly journals Hybrid Synchronization of Uncertain Generalized Lorenz System by Adaptive Control

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Xinlian Zhou ◽  
Yuhua Xu
Keyword(s):  
Adaptive Control ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Reduced Order ◽  
Parameter Update Law ◽  
Generalized Lorenz System ◽  
Stability Point ◽  
Modified Projective Synchronization ◽  
Hybrid Synchronization ◽  
The Stability

This paper investigates hybrid synchronization of the uncertain generalized Lorenz system. Several useful criteria are given for synchronization of two generalized Lorenz systems, and the adaptive control law and the parameter update law are used. In comparison with those of existing synchronization methods, hybrid synchronization includes full-order synchronization, reduced-order synchronization, and modified projective synchronization. What is more, control of the stability point, complete synchronization, and antisynchronization can coexist in the same system. Numerical simulations show the effectiveness of this method in a class of chaotic systems.

scholarly journals Hybrid Projective Synchronization of 4-D Hyperchaotic Systems via Adaptive Control

2020 ◽  
Vol 12 (2) ◽  
pp. 201-208
Author(s):  
A. Khan ◽  
H. Chaudhary
Keyword(s):  
Adaptive Control ◽  
Asymptotic Stability ◽  
Secure Communication ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Control Technique ◽  
Complete Agreement ◽  
Suggested Technique ◽  
Hybrid Projective Synchronization ◽  
Hyperchaotic Systems

This paper designs a procedure for investigating the hybrid projective synchronization (HPS) scheme between two identical 4-D hyperchaotic systems. Based on Lyapunov stability theory (LST), an adaptive control technique (ACT) has been designed to achieve the desired HPS scheme. The suggested technique determines globally the asymptotic stability and identification of parameters simultaneously using HPS scheme. It is noted that complete , hybrid and anti-synchronization turns into particular cases of HPS scheme. Numerical simulations are presented to validate the effectivity and feasibleness of the considered technique by using MATLAB. Remarkably, the theoretical and computational outcomes are in complete agreement. Also, the considered HPS scheme is very efficient as it has numerous applications in encryption and secure communication.

Function projective synchronization of two four-scroll hyperchaotic systems with unknown parameters

Open Physics ◽  
2013 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhenwu Sun
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
System Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Hyperchaotic Systems

AbstractFunction projective synchronization (FPS) of two novel hyperchaotic systems with four-scroll attractors which have been found up to the present is investigated. Adaptive control is employed in the situation that system parameters are unknown. Based on Lyapunov stability theory, an adaptive controller and a parameter update law are designed so that the two systems can be synchronized asymptotically by FPS. Numerical simulation is provided to show the effectiveness of the proposed adaptive controller and the parameter update law.

Modified Projective Synchronization of Chaotic Systems with Unknown Parameters

2011 ◽  
Vol 128-129 ◽  
pp. 1182-1185
Author(s):  
Min Xiu Yan ◽  
Li Ping Fan
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Adaptive Sliding Mode Control ◽  
Unknown Parameters ◽  
Response System ◽  
Uncertain Chaotic Systems ◽  
Modified Projective Synchronization

This paper proposes the modified projective synchronization of uncertain chaotic systems with unknown parameters via active adaptive sliding mode control (AASMC). The disturbances are considered both in the drive and the response system. The bounds of the disturbances are unknown. The adaptive updating laws are designed to tackle the unknown parameters. Moreover, the robustness and stability of the proposed AASMC is proved by the Lyapunov stability theory. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed scheme.

scholarly journals Generation and Modified Projective Synchronization for a Class of New Hyperchaotic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Nuo Jia ◽  
Tao Wang
Keyword(s):  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Time Varying ◽  
Control Methods ◽  
Unknown Parameters ◽  
Control Scheme ◽  
Time Varying Parameters ◽  
Modified Projective Synchronization ◽  
Adaptive Control Strategy ◽  
Hyperchaotic Systems

A class of new hyperchaotic systems with different nonlinear terms is proposed, and the existence of hyperchaos is exhibited by calculating their Lyapunov exponent spectrums. Then the universal theories on modified projective synchronization (MPS) of the systems with general form which linearly depends on unknown parameters or time-varying parameters, are investigated by presenting an adaptive control strategy together with parameter update laws and a nonlinear control scheme based on Lyapunov stability theory. Subsequently, the presented control methods are applied to achieve MPS of the new hyperchaotic systems, and their effectiveness is illustrated by numerical simulations.

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