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.

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.

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 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.

SYNCHRONIZATION OF COMPLEX-VARIABLE DYNAMICAL NETWORKS WITH COMPLEX COUPLING

2013 ◽  
Vol 24 (02) ◽  
pp. 1350007 ◽  
Author(s):  
ZHAOYAN WU ◽  
XINCHU FU
Keyword(s):  
Complex Variable ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Control Scheme ◽  
General Network ◽  
Adaptive Coupling ◽  
Theoretical Results

In this paper, synchronization of complex-variable dynamical networks with complex coupling is investigated. An adaptive feedback control scheme is adopted to design controllers for achieving synchronization of a general network with both complex inner and outer couplings. For a network with only complex inner or outer coupling, pinning control and adaptive coupling strength methods are adopted to achieve synchronization under some assumptions. Several synchronization criteria are derived based on Lyapunov stability theory. Numerical simulations are provided to verify the effectiveness of the theoretical results.

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.

scholarly journals Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Soup Tewa Kammogne ◽  
Hilaire Bertrand Fotsin
Keyword(s):  
Additive White Gaussian Noise ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Systematic Design ◽  
Modified Projective Synchronization ◽  
Robust Adaptive ◽  
Robust Adaptive Synchronization

A method of estimation of all parameters of a class of nonlinear uncertain dynamical systems is considered, based on the modified projective synchronization (MPS). The case of modified Colpitts oscillators is investigated. Through a suitable transformation of the dynamical system, sufficient conditions for achieving synchronization are derived based on Lyapunov stability theory. Global stability and asymptotic robust synchronization of the considered system are investigated. The proposed approach offers a systematic design procedure for robust adaptive synchronization of a large class of chaotic systems. The combined effect of both an additive white Gaussian noise (AWGN) and an artificial perturbation is numerically investigated. Results of numerical simulations confirm the effectiveness of the proposed control strategy.

Hybrid Delayed Synchronizations of Complex Chaotic Systems in Modulus-Phase Spaces and Its Application

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
Luo Chao
Keyword(s):  
Secure Communication ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Complete Synchronization ◽  
Modified Projective Synchronization ◽  
Synchronization Scheme ◽  
Complex Chaotic Systems ◽  
Real Number Field

Compared with chaotic systems over the real number field, complex chaotic dynamics have some unique properties. In this paper, a kind of novel hybrid synchronizations of complex chaotic systems is discussed analytically and numerically. Between two nonidentical complex chaotic systems, modified projective synchronization (MPS) in the modulus space and complete synchronization in the phase space are simultaneously achieved by means of active control. Based on the Lyapunov stability theory, a controller is developed, in which time delay as an important consideration is involved. Furthermore, a switch-modulated digital secure communication system based on the proposed synchronization scheme is carried out. Different from the previous works, only one set of drive-response chaotic systems can implement switch-modulated secure communication, which could simplify the complexity of design. Furthermore, the latency of a signal transmitted between transmitter and receiver is simulated by channel delay. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

Stability analysis and modified projective synchronization of fractional-order hyperchaotic dynamical systems using nonlinear controllers

2021 ◽  
pp. 2150081
Author(s):  
S. Saha Ray
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Direct Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hurwitz Stability ◽  
Modified Projective Synchronization ◽  
Error Dynamics ◽  
The Stability ◽  
Hyperchaotic Systems

This paper deals with the modified projective synchronization between two fractional-order four-dimensional (4D) hyperchaotic systems. Based on the Lyapunov stability theory, a new controller for the synchronization of two fractional-order hyperchaotic systems is developed. The stability analysis of the error dynamics system is performed by the fractional-order Lyapunov direct method alongwith Routh–Hurwitz stability criterion. Numerical simulations are presented to demonstrate the validity and verify the effectiveness of the proposed synchronization scheme.

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