A Three-Dimensional No-Equilibrium Chaotic System: Analysis, Synchronization and Its Fractional Order Form

2017 ◽  
pp. 449-470 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Sundarapandian Vaidyanathan ◽  
Christos K. Volos ◽  
Ahmad Taher Azar ◽  
Thang Manh Hoang ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
System Analysis ◽  
Three Dimensional ◽  
Order Form

scholarly journals New Fractional Order Chaotic System: Analysis, Synchronization, and it’s Application

2021 ◽  
Vol 17 (1) ◽  
pp. 1-9
Author(s):  
Zain_Aldeen Rahman ◽  
Basil Jassim ◽  
Yasir Al_Yasir
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
System Analysis ◽  
Three Dimensional ◽  
Nonlinear Dynamic System ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Communication Scheme ◽  
New System

In this paper, a new nonlinear dynamic system, new three-dimensional fractional order complex chaotic system, is presented. This new system can display hidden chaotic attractors or self-excited chaotic attractors. The Dynamic behaviors of this system have been considered analytically and numerically. Different means including the equilibria, chaotic attractor phase portraits, the Lyapunov exponent, and the bifurcation diagrams are investigated to show the chaos behavior in this new system. Also, a synchronization technique between two identical new systems has been developed in master- slave configuration. The two identical systems are synchronized quickly. Furthermore, the master-slave synchronization is applied in secure communication scheme based on chaotic masking technique. In the application, it is noted that the message is encrypted and transmitted with high security in the transmitter side, in the other hand the original message has been discovered with high accuracy in the receiver side. The corresponding numerical simulation results proved the efficacy and practicability of the developed synchronization technique and its application

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

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 Basin of Attraction Analysis of New Memristor-Based Fractional-Order Chaotic System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Long Ding ◽  
Li Cui ◽  
Fei Yu ◽  
Jie Jin
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Fractional Order ◽  
Chaotic System ◽  
Exponential Function ◽  
Local Minimum ◽  
System Analysis ◽  
Basin Of Attraction ◽  
Stable Point ◽  
The Basin Of Attraction

Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

A chaotic system with equilibria located on a line and its fractional-order form

2022 ◽  
pp. 35-62
Author(s):  
Karthikeyan Rajagopal ◽  
Fahimeh Nazarimehr ◽  
Alireza Bahramian ◽  
Sajad Jafari
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Form

A Novel 3D Fractional-Order Chaotic System with Multifarious Coexisting Attractors

2019 ◽  
Vol 29 (01) ◽  
pp. 1950004 ◽  
Author(s):  
Chengyi Zhou ◽  
Zhijun Li ◽  
Yicheng Zeng ◽  
Sen Zhang
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Order System ◽  
Attractive Feature ◽  
Huge Amount ◽  
Coexisting Attractors ◽  
Interesting Phenomenon ◽  
Periodic Attractors

A novel three-dimensional fractional-order autonomous chaotic system marked by the ample and complex coexisting attractors is presented. There are a total of seven terms including four nonlinearities in the new system. The evolution of coexisting attractors of the system are numerically investigated by considering both the fractional-order and other system parameters as bifurcation parameters. Numerical simulation results indicate that the system has a huge amount of multifarious coexisting strange attractors for various ranges of parameters, including coexisting point, periodic attractors, multifarious coexisting chaotic, and periodic attractors. Compared with other chaotic systems, the biggest difference and most attractive feature is the capability of the proposed fractional-order system to produce coexisting attractors that undergo a simultaneous displacement phenomenon with variation of a single parameter. Moreover, it is worth noting that constant Lyapunov exponents and the interesting phenomenon of transient coexisting attractors are also observed. Finally, the corresponding implementation circuit is designed. The consistency of the hardware experimental results with numerical simulations verifies the feasibility of the new fractional-order chaotic system.

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