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 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.

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 Harmonic Balance Method for Chaotic Dynamics in Fractional-Order Rössler Toroidal System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Huijian Zhu
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Harmonic Balance ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Chaotic Motions ◽  
Behavior Based

This paper deals with the problem of determining the conditions under which fractional order Rössler toroidal system can give rise to chaotic behavior. Based on the harmonic balance method, four detailed steps are presented for predicting the existence and the location of chaotic motions. Numerical simulations are performed to verify the theoretical analysis by straightforward computations.

scholarly journals Synchronization for a Class of Fractional-Order Hyperchaotic System and Its Application

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Wen Tan ◽  
Feng Ling Jiang ◽  
Chuang Xia Huang ◽  
Lan Zhou
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Secure Communication ◽  
Controller Design ◽  
Design Method ◽  
Hyperchaotic System ◽  
Response System ◽  
Control Scheme ◽  
The Stability ◽  
Hyperchaotic Systems

A new controller design method is proposed to synchronize the fractional-order hyperchaotic system through the stability theory of fractional calculus; the synchronization between two identical fractional-order Chen hyperchaotic systems is realized by designing only two suitable controllers in the response system. Furthermore, this control scheme can be used in secure communication via the technology of chaotic masking using the complex nonperiodic information as trial message, and the useful information can be recovered at the receiver. Numerical simulations coincide with the theoretical analysis.

scholarly journals A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Duy Vo Hoang ◽  
Sifeu Takougang Kingni ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Chaotic Attractors ◽  
Dimensional System ◽  
Hyperchaotic System ◽  
Equilibrium System ◽  
Coexisting Attractors ◽  
Amplitude Control ◽  
Dynamical Behaviors ◽  
Point Attractor

No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.

A Fractional-Order Hyperchaotic System and its Circuit Implement

2014 ◽  
Vol 701-702 ◽  
pp. 1143-1147
Author(s):  
Qi Li Wang
Keyword(s):  
Fractional Order ◽  
Strange Attractor ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Order System ◽  
Hyperchaotic System ◽  
Dynamical Properties ◽  
Simulation Results ◽  
Sensitivity To Initial Conditions

A fractional-order hyperchaotic system was proposed and some basic dynamical properties were investigated to show chaotic behavior. These properties include instability of equilibria, sensitivity to initial conditions, strange attractor, Lyapunov exponents, and bifurcation. The fractional-order system presents hyperchaos, chaos, and periodic behavior when the parameters vary continuously. Then, an analog circuit is designed onMultisim 11and the Multisim results are agreed with the simulation results.

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.

A Hyperchaotic System and its Synchronization via Scalar Controller

2011 ◽  
Vol 50-51 ◽  
pp. 254-257
Author(s):  
Wu Chun Dai ◽  
Zheng Fu Cheng
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Exponents ◽  
Mathematical Proof ◽  
Hyperchaotic System ◽  
Scalar Control ◽  
Response System ◽  
Dynamical Behaviors ◽  
Synchronization Scheme ◽  
New Hyperchaotic System

In this paper, a 4D hyperchaotic system is proposed. Some basic dynamical behaviors are explored by calculating its Lyapunov exponents, Poincar´e mapping, etc.. Finally, synchronization for this new hyperchaotic system is achieved via scalar control. The nonlinear terms in the response system are not dropped. The proposed synchronization scheme is simple and theoretically rigorous. The mathematical proof of this method is provided. Some numerical simulations are obtained. The numerical simulations coincide with the theoretical analysis.

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