scholarly journals Effective Synchronization of a Class of Chua’s Chaotic Systems Using an Exponential Feedback Coupling

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Patrick Louodop ◽  
Hilaire Fotsin ◽  
Elie B. Megam Ngouonkadi ◽  
Samuel Bowong ◽  
Hilda A. Cerdeira
Keyword(s):  
Computer Simulations ◽  
Lyapunov Stability ◽  
Exponential Function ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Response Systems ◽  
The Stability ◽  
Systems Framework

A robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.

Stability Analysis on S Plane Control of Underwater Vehicles

2013 ◽  
Vol 437 ◽  
pp. 716-721 ◽  
Author(s):  
Yue Ming Li ◽  
Ying Hao Zhang ◽  
Guo Cheng Zhang ◽  
Zhong Hui Hu
Keyword(s):  
Stability Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Underwater Vehicles ◽  
Velocity Control ◽  
Position Controller ◽  
The Stability

This paper addresses the stability analysis on S Plane Control in terms of both position and velocity control. Employing Lyapunov stability theory and T-passivity theory, this paper proves the stability of the position controller based on S Plane Control, and on this ground, the stability analysis of the velocity controller based on S Plane Control is done. Finally, the S Plane Control results obtained from the sea trials are given.

scholarly journals On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Lyapunov Stability ◽  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Nonlinear Control Method

The problems of full-state hybrid projective synchronization (FSHPS) and inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems are investigated in 2D. Based on nonlinear control method and Lyapunov stability theory, new controllers are designed to study FSHPS and IFSHPS, respectively, for 2D arbitrary chaotic systems in discrete-time. Numerical example and simulations are used to validate the main results of this paper.

scholarly journals The Synchronization of N Cascade-Coupled Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Pengyu Li ◽  
Juan Du ◽  
Shouliang Li ◽  
Yazhao Zheng ◽  
Bowen Jia
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
General Criterion ◽  
Synchronization Method ◽  
Bidirectional Coupling ◽  
Coupling Parameters

In this paper, we investigate a novel synchronization method, which consists of nn≥2 cascade-coupled chaotic systems. Furthermore, as the number of chaotic systems decreases from n to 2, the proposed synchronization will transform into bidirectional coupling synchronization. Based on Lyapunov stability theory, a general criterion is proposed for choosing the appropriate coupling parameters to ensure cascading synchronization. Moreover, 4 Lü systems are taken as an example and the corresponding numerical simulations demonstrate the effectiveness of our idea.

DIGITAL CRYPTOGRAPHY AND FEEDBACK SYNCHRONIZATION OF CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (04) ◽  
pp. 521-529 ◽  
Author(s):  
MALA MITRA ◽  
SANTO BANERJEE
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Coupled System ◽  
Lyapunov Stability Theory ◽  
Chaotic Synchronization ◽  
Feedback Controller ◽  
New Method ◽  
Secure Communications

Secure communications via chaotic synchronization is demonstrated in this literature. At first we have designed a feedback controller for chaotic synchronization utilizing the Lyapunov stability theory for cascade-connected systems.The method has been applied successfully to make two identical systems globally asymptotically synchronized. The result of numerical simulations are given to validate the effectiveness of this method. Then we have discussed a new method of cryptography for this coupled system which is very simple to implement and effective.

scholarly journals Adaptive Synchronization of Chaotic SC-CNN with Uncertain State Template

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Phuong Dam Thanh ◽  
Cat Pham Thuong
Keyword(s):  
Neural Network ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Cellular Neural Network ◽  
Uncertain Parameter ◽  
Adaptive Synchronization ◽  
Chaotic State ◽  
Control Laws

The problem of synchronization of chaotic State Controlled Cellular Neural Network (SC-CNN) with uncertain state template is investigated. In detail, the following three cases are solved: firstly, synchronization of two identical chaotic SC-CNNs with uncertain state template, secondly, synchronization of two nonidentical chaotic SC-CNNs with all uncertain state templates, and, thirdly, synchronization between chaotic SC-CNN with uncertain state template and different uncertain parameter chaotic systems. The controllers and update laws proposed in each case are proved closely based on Lyapunov stability theory. In addition, some illustrative corresponding examples are presented to demonstrate the effectiveness and usefulness of the proposed control laws.

Dual Combination Synchronization of Six Chaotic Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Junwei Sun ◽  
Suxia Jiang ◽  
Guangzhao Cui ◽  
Yanfeng Wang
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Combination Synchronization

Based on combination synchronization of three chaotic systems and combination–combination synchronization of four chaotic systems, a novel scheme of dual combination synchronization is investigated for six chaotic systems in the paper. Using combined adaptive control and Lyapunov stability theory of chaotic systems, some sufficient conditions are attained to realize dual combination synchronization of six chaotic systems. The corresponding theoretical proofs and numerical simulations are presented to demonstrate the effectiveness and correctness of the dual combination synchronization. Due to the complexity of dual combination synchronization, it will be more secure and interesting to transmit and receive signals in application of communication.

Synchronization of spatiotemporal networks via backstepping using neighbor information

2016 ◽  
Vol 27 (11) ◽  
pp. 1650129 ◽  
Author(s):  
Shuang Liu ◽  
Yuan Chai ◽  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Recurrence Relation ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Complex Dynamical Networks ◽  
Control Input ◽  
Dynamical Networks

A backstepping scheme is proposed for synchronization between two complex dynamical networks with different structures. The nodes of the networks are spatiotemporal chaotic systems. A recurrence relation containing the information from neighbors is established so that only one control input is needed to synchronize two spatiotemporal networks. The Lyapunov stability theory is applied to prove that the differences between the drive and response networks tend to zero asymptotically under the control. The proposed scheme is numerically implemented in the synchronization of two networks with the Fisher–Kolmogorov and the Burgers spatiotemporal chaotic systems as the nodes.

Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems based on Fractional Lyapunov Stability Theory

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Order ◽  
Lyapunov Stability ◽  
Finite Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Convergence Time ◽  
Control Approach ◽  
Finite Time Stability

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.

scholarly journals Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

2014 ◽  
Vol 65 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Rajagopal Karthikeyan ◽  
Vaidyanathan Sundarapandian
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Hybrid Synchronization ◽  
Active Control Method

Abstract This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

scholarly journals Synchronization of Fractional-Order Hyperchaotic Systems via Fractional-Order Controllers

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Tianzeng Li ◽  
Yu Wang ◽  
Yong Yang
Keyword(s):  
Fractional Order ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Control Parameters ◽  
Optimal Value ◽  
Fractional Order Controller ◽  
Hyperchaotic Systems

In this paper, the synchronization of fractional-order chaotic systems is studied and a new fractional-order controller for hyperchaos synchronization is presented based on the Lyapunov stability theory. The proposed synchronized method can be applied to an arbitrary four-dimensional fractional hyperchaotic system. And we give the optimal value of control parameters to achieve synchronization of fractional hyperchaotic system. This approach is universal, simple, and theoretically rigorous. Numerical simulations of several fractional-order hyperchaotic systems demonstrate the universality and the effectiveness of the proposed method.

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