scholarly journals Theoretical Analysis and Adaptive Synchronization of a 4D Hyperchaotic Oscillator

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
T. Fonzin Fozin ◽  
J. Kengne ◽  
F. B. Pelap
Keyword(s):  
Mathematical Model ◽  
Adaptive Control ◽  
Theoretical Analysis ◽  
Electronic Circuit ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Exponential Nonlinearity ◽  
Dynamical Properties ◽  
Hyperchaotic Systems ◽  
Good Agreement

We propose a new mathematical model of the TNC oscillator and study its impact on the dynamical properties of the oscillator subjected to an exponential nonlinearity. We establish the existence of hyperchaotic behavior in the system through theoretical analysis and by exploiting electronic circuit experiments. The obtained numerical results are found to be in good agreement with experimental observations. Moreover, the new technique on adaptive control theory is used on our model and it is rigorously proven that the adaptive synchronization can be achieved for hyperchaotic systems with uncertain parameters.

scholarly journals Implementation on Electronic Circuits and RTR Pragmatical Adaptive Synchronization: Time-Reversed Uncertain Dynamical Systems' Analysis and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shih-Yu Li ◽  
Cheng-Hsiung Yang ◽  
Li-Wei Ko ◽  
Chin-Teng Lin ◽  
Zheng-Ming Ge
Keyword(s):  
Adaptive Control ◽  
Stability Theory ◽  
Initial Conditions ◽  
Stability Theorem ◽  
Phase Portraits ◽  
Adaptive Synchronization ◽  
Complex Signal ◽  
Uncertain Parameters ◽  
Chaotic Motions ◽  
Lorentz System

We expose the chaotic attractors of time-reversed nonlinear system, further implement its behavior on electronic circuit, and apply the pragmatical asymptotically stability theory to strictly prove that the adaptive synchronization of given master and slave systems with uncertain parameters can be achieved. In this paper, the variety chaotic motions of time-reversed Lorentz system are investigated through Lyapunov exponents, phase portraits, and bifurcation diagrams. For further applying the complex signal in secure communication and file encryption, we construct the circuit to show the similar chaotic signal of time-reversed Lorentz system. In addition, pragmatical asymptotically stability theorem and an assumption of equal probability for ergodic initial conditions (Ge et al., 1999, Ge and Yu, 2000, and Matsushima, 1972) are proposed to strictly prove that adaptive control can be accomplished successfully. The current scheme of adaptive control—by traditional Lyapunov stability theorem and Barbalat lemma, which are used to prove the error vector—approaches zero, as time approaches infinity. However, the core question—why the estimated or given parameters also approach to the uncertain parameters—remains without answer. By the new stability theory, those estimated parameters can be proved approaching the uncertain values strictly, and the simulation results are shown in this paper.

Function Projective Dual Synchronization with Uncertain Parameters of Hyperchaotic Systems

2017 ◽  
Vol 6 (4) ◽  
pp. 1-16 ◽  
Author(s):  
A. Almatroud Othman ◽  
M.S.M. Noorani ◽  
M. Mossa Al-sawalha
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lu System ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

Function projective dual synchronization between two pairs of hyperchaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the Lyapunov stability theory, a suitable and effective adaptive control law and parameters update rule for unknown parameters are designed, such that function projective dual synchronization between the hyperchaotic Chen system and the hyperchaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

A New Dynamic System Analysis

2013 ◽  
Vol 392 ◽  
pp. 222-226
Author(s):  
Bao Liang Mi ◽  
Guo Zeng Wu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Dynamic System ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
System Analysis ◽  
Electronic Circuit ◽  
Circuit Implementation ◽  
Dynamical Properties ◽  
Electronic Circuit Implementation

A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation.

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC CHEN SYSTEM

2008 ◽  
Vol 22 (08) ◽  
pp. 1015-1023 ◽  
Author(s):  
XINGYUAN WANG ◽  
XIANGJUN WU
Keyword(s):  
Adaptive Control ◽  
Parameter Identification ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Uncertain Parameters ◽  
Chen System ◽  
Adaptive Control Law

This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

scholarly journals Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 304-313 ◽  
Author(s):  
M. Mossa Al-Sawalha ◽  
Ayman Al-Sawalha
Keyword(s):  
Adaptive Control ◽  
Dynamical Systems ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Adaptive Laws ◽  
Analytic Expression ◽  
Hyperchaotic Systems

AbstractThe objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. Theoretical analysis and numerical simulations are shown to verify the results.

scholarly journals A research on adaptive control to stabilize and synchronize a hyperchaotic system with uncertain parameters

2015 ◽  
Vol 5 (2) ◽  
pp. 51-62 ◽  
Author(s):  
Israr Ahmad ◽  
Azizan Bin Saaban ◽  
Adyda Binti Ibrahim ◽  
Said Al-Hadhrami ◽  
Mohammad Shahzad ◽  
...  
Keyword(s):  
Adaptive Control ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Closed Loop System ◽  
Complete Synchronization ◽  
Nonlinear Controllers ◽  
Control And Synchronization ◽  
Hyperchaotic Systems

This paper addresses the chaos control and synchronization problems of a hyperchaotic system. It is assumed that the parameters of the hyperchaotic system are unknown and the system is perturbed by the external disturbance. Based on the Lyapunov stability theory and the adaptive control theory, suitable nonlinear controllers are designed for the asymptotic stability of the closed-loop system both for stabilization of hyperchaos at the origin and complete synchronization of two identical hyperchaotic systems. Accordingly, suitable update laws are proposed to estimate the fully uncertain parameters. All simulation results are carried out to validate the effectiveness of the theoretical findings. The effect of external disturbance is under our discussion.

GENERALIZED PROJECTIVE SYNCHRONIZATION AND PARAMETERS ESTIMATION OF TWO NEW HYPERCHAOTIC SYSTEMS WITH FULLY UNCERTAIN PARAMETERS

2010 ◽  
Vol 21 (02) ◽  
pp. 249-259 ◽  
Author(s):  
CONG-XU ZHU
Keyword(s):  
Adaptive Control ◽  
Adaptive Controller ◽  
Stability Theorem ◽  
Parameters Estimation ◽  
Projective Synchronization ◽  
Uncertain Parameters ◽  
Lyapunov Stability Theorem ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems ◽  
Theoretical Results

This paper investigates adaptive generalized projective synchronization (GPS) between two novel hyperchaotic systems with different structure and fully uncertain parameters. Based on the Lyapunov stability theorem and the adaptive control theory, GPS between the two hyperchaotic systems is achieved by proposing a new adaptive controller and a novel parameters estimation update law. Strict theoretical proof is put forward. Numerical simulations are presented to demonstrate the effectiveness of the proposed GPS scheme and verify the theoretical results.

scholarly journals Passivity-Based Adaptive Hybrid Synchronization of a New Hyperchaotic System with Uncertain Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Xiaobing Zhou ◽  
Zhangbiao Fan ◽  
Dongming Zhou ◽  
Xiaomei Cai
Keyword(s):  
Numerical Simulation ◽  
Parameter Estimation ◽  
Adaptive Control ◽  
Control Theory ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Synchronization Problem ◽  
Hybrid Synchronization ◽  
New Hyperchaotic System ◽  
Hyperchaotic Systems

We investigate the adaptive hybrid synchronization problem for a new hyperchaotic system with uncertain parameters. Based on the passivity theory and the adaptive control theory, corresponding controllers and parameter estimation update laws are proposed to achieve hybrid synchronization between two identical uncertain hyperchaotic systems with different initial values, respectively. Numerical simulation indicates that the presented methods work effectively.

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