scholarly journals Analysis and Synchronization of a New Hyperchaotic System with Exponential Term

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3281
Author(s):  
Shunjie Li ◽  
Yawen Wu ◽  
Xuebing Zhang
Keyword(s):  
Chaotic Behavior ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Hyperchaotic System ◽  
Global Synchronization ◽  
Exponential Term ◽  
Synchronization Problem ◽  
Line Of Equilibria ◽  
New Hyperchaotic System ◽  
Adaptive Control Law

In this paper, a new four-dimensional hyperchaotic system with an exponential term is presented. The basic dynamical properties and chaotic behavior of the new attractor are analyzed. It can be shown that this system possesses either a line of equilibria or a single one. The existence of hyperchaos is confirmed by its Lyapunov exponents. Moreover, the synchronization problem for the hyperchaotic system is studied. Based on the Lyapunov stability theory, an adaptive control law with two inputs is proposed to achieve the global synchronization. Numerical simulations are given to validate the correctness of the proposed control law.

scholarly journals Finite-Time Adaptive Synchronization of a New Hyperchaotic System with Uncertain Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ma Yongguang ◽  
Dong Zijian
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Hyperchaotic System ◽  
Finite Time Stability ◽  
Synchronization Scheme ◽  
New Hyperchaotic System ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

This paper presents a finite-time adaptive synchronization strategy for a class of new hyperchaotic systems with unknown slave system’s parameters. Based on the finite-time stability theory, an adaptive control law is derived to make the states of the new hyperchaotic systems synchronized in finite-time. Numerical simulations are presented to show the effectiveness of the proposed finite time synchronization scheme.

CHAOS SYNCHRONIZATION OF TWO COUPLED DYNAMOS SYSTEMS WITH UNKNOWN SYSTEM PARAMETERS

2004 ◽  
Vol 15 (06) ◽  
pp. 873-883 ◽  
Author(s):  
H. N. AGIZA
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Error Feedback ◽  
Simple Criterion ◽  
Global Synchronization ◽  
System Parameters ◽  
Synchronization Problem ◽  
Unknown System

This paper addresses the synchronization problem of two coupled dynamos systems in the presence of unknown system parameters. Based on Lyapunov stability theory, an active control law is derived and activated to achieve the state synchronization of two identical coupled dynamos systems. By using Gerschgorin theorem, a simple generic criterion is derived for global synchronization of two coupled dynamos systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems, where only a few algebraic inequalities are involved. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.

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.

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 Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-23 ◽  
Author(s):  
Li Xiong ◽  
Zhenlai Liu ◽  
Xinguo Zhang
Keyword(s):  
Secure Communication ◽  
Control Method ◽  
Dynamical Behavior ◽  
Control Level ◽  
Lyapunov Stability Theory ◽  
Dynamical Analysis ◽  
Linear Feedback ◽  
Hyperchaotic System ◽  
Error System ◽  
New Hyperchaotic System

This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz.

Synchronization control of complex dynamical networks with piecewise constant arguments

2018 ◽  
Vol 41 (2) ◽  
pp. 540-551 ◽  
Author(s):  
Tianhu Yu ◽  
Menglong Su
Keyword(s):  
Impulsive Control ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Control Law ◽  
Dynamical Networks ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Synchronization Problem ◽  
Theoretical Results

The pinning synchronization problem is investigated for complex dynamical networks with hybrid coupling via impulsive control. Based on the Lyapunov stability theory, some novel synchronization criteria are derived and an impulsive pinning control law is proposed. By introducing a differential inequality for systems with piecewise constant arguments, it is not necessary to establish any relationship between the norms of the error states with or without piecewise constant arguments. Typical numerical examples are utilized to illustrate the validity and improvements as regards conservativeness of the theoretical results.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

2018 ◽  
Vol 7 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Hamed Tirandaz
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Parameters Estimation ◽  
Control Law ◽  
Complete Control ◽  
Synchronization Problem ◽  
Control And Synchronization ◽  
Adaptive Control Law

Abstract Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

scholarly journals Theoretical Analysis and Circuit Verification for Fractional-Order Chaotic Behavior in a New Hyperchaotic System

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ling Liu ◽  
Chongxin Liu
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Circuit Diagram ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Dynamical Behaviors ◽  
Mapping Parameter ◽  
New Hyperchaotic System ◽  
Observation Results

A novel nonlinear four-dimensional hyperchaotic system and its fractional-order form are presented. Some dynamical behaviors of this system are further investigated, including Poincaré mapping, parameter phase portraits, equilibrium points, bifurcations, and calculated Lyapunov exponents. A simple fourth-channel block circuit diagram is designed for generating strange attractors of this dynamical system. Specifically, a novel network module fractance is introduced to achieve fractional-order circuit diagram for hardware implementation of the fractional attractors of this nonlinear hyperchaotic system with order as low as 0.9. Observation results have been observed by using oscilloscope which demonstrate that the fractional-order nonlinear hyperchaotic attractors exist indeed in this new system.

scholarly journals Adaptive Synchronization for Hyperchaotic Liu System

2022 ◽  
Vol 9 ◽  
Author(s):  
Shunjie Li ◽  
Yawen Wu ◽  
Gang Zheng
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Chaos Synchronization ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Control Schemes ◽  
Liu System ◽  
Adaptive Control Law

In this paper, the adaptive control design is investigated for the chaos synchronization of two identical hyperchaotic Liu systems. First, an adaptive control law with two inputs is proposed based on Lyapunov stability theory. Secondly, two other control schemes are obtained based on a further analysis of the proposed adaptive control law. Finally, numerical simulations are presented to validate the effectiveness and correctness of these results.

scholarly journals APPLICATION OF LEARNING FEED-FORWARD CONTROLLER BASED ON MODEL REFERENCE ADAPTIVE SYSTEM FOR MISSILE STABILIZATION

2021 ◽  
Vol 1 (4(68)) ◽  
pp. 34-39
Author(s):  
V. Nguyen ◽  
C. Dang ◽  
V. Luong
Keyword(s):  
Adaptive System ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Model Reference ◽  
Feed Forward ◽  
Model Reference Adaptive System ◽  
Feed Forward Controller ◽  
Model Reference Adaptive ◽  
Adaptive Control Law ◽  
Research Analysis

The article presents the results of research, analysis and how to build learning feed-forward controller based on model reference adaptive system in the remote control loop for missile stabilization. The controller structure is simple, adaptive control law applying Lyapunov stability theory fast convergence and sustainable. The simulation results have shown the advantages of using algorithm, the missile is always stable when there is a parameter change due to the effects of flight conditions.

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