Fractional Order Adaptive Synchronization of a New Hyperchaotic System with an Uncertain Parameter

2009 ◽  
Author(s):  
Longge Zhang
Keyword(s):  
Fractional Order ◽  
Uncertain Parameter ◽  
Adaptive Synchronization ◽  
Hyperchaotic System ◽  
New Hyperchaotic System

Adaptive synchronization of a hyperchaotic system with uncertain parameter

2006 ◽  
Vol 30 (5) ◽  
pp. 1133-1142 ◽  
Author(s):  
E.M. Elabbasy ◽  
H.N. Agiza ◽  
M.M. El-Dessoky
Keyword(s):  
Uncertain Parameter ◽  
Adaptive Synchronization ◽  
Hyperchaotic System

A New Five Dimensional Hyperchaotic System and its Fractional Order Form

2013 ◽  
Vol 464 ◽  
pp. 375-380 ◽  
Author(s):  
Ling Liu ◽  
Chong Xin Liu ◽  
Yi Fan Liao
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Order Form ◽  
Simulation Results ◽  
Predictor Corrector ◽  
New Hyperchaotic System

In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.

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.

Adaptive synchronization of a new hyperchaotic system with uncertain parameters

2007 ◽  
Vol 33 (3) ◽  
pp. 922-928 ◽  
Author(s):  
Tiegang Gao ◽  
Zengqiang Chen ◽  
Zhuzhi Yuan ◽  
Dongchuan Yu
Keyword(s):  
Adaptive Synchronization ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
New Hyperchaotic System

scholarly journals Adaptive Inverse Optimal Control of a Novel Fractional-Order Four-Wing Hyperchaotic System with Uncertain Parameter and Circuitry Implementation

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Chaojun Wu ◽  
Gangquan Si ◽  
Yanbin Zhang ◽  
Ningning Yang
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
State Feedback ◽  
Feedback Controller ◽  
Uncertain Parameter ◽  
Hyperchaotic System ◽  
Inverse Optimal Control ◽  
State Feedback Controller ◽  
Oscillation Circuit ◽  
Order Four

An efficient approach of inverse optimal control and adaptive control is developed for global asymptotic stabilization of a novel fractional-order four-wing hyperchaotic system with uncertain parameter. Based on the inverse optimal control methodology and fractional-order stability theory, a control Lyapunov function (CLF) is constructed and an adaptive state feedback controller is designed to achieve inverse optimal control of a novel fractional-order hyperchaotic system with four-wing attractor. Then, an electronic oscillation circuit is designed to implement the dynamical behaviors of the fractional-order four-wing hyperchaotic system and verify the satisfactory performance of the controller. Comparing with other fractional-order chaos control methods which may have more than one nonlinear state feedback controller, the inverse optimal controller has the advantages of simple structure, high reliability, and less control effort that is required and can be implemented by electronic oscillation circuit.

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

2016 ◽  
Vol 2016 ◽  
pp. 1-3 ◽  
Author(s):  
Jay Prakash Singh ◽  
B. K. Roy
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Hyperchaotic System ◽  
Initial Condition ◽  
Circuit Verification ◽  
System L ◽  
Periodic Behaviour ◽  
New Hyperchaotic System

Some comments on the paper “Theoretical Analysis and Circuit Verification for Fractional-Order Chaotic Behavior in a New Hyperchaotic System” (L. Liu and C. Liu, 2014) are pointed out in this letter. It is shown in this letter that the claimed hyperchaotic system exhibits a periodic behaviour for the chosen parameters and initial condition. However, the claimed hyperchaotic system exhibits chaotic behaviours for some other parameters.

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.

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