A novel finite‐time terminal observer of a fractional‐order chaotic system with chaos entanglement function

2021 ◽  
Author(s):  
Ayub Khan ◽  
Nasreen Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time

scholarly journals Finite-Time Synchronizing Fractional-Order Chaotic Volta System with Nonidentical Orders

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Jian-Bing Hu ◽  
Ling-Dong Zhao
Keyword(s):  
Fractional Calculus ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Fractional Differentiation ◽  
Fractional Chaotic System

We investigate synchronizing fractional-order Volta chaotic systems with nonidentical orders in finite time. Firstly, the fractional chaotic system with the same structure and different orders is changed to the chaotic systems with identical orders and different structure according to the property of fractional differentiation. Secondly, based on the lemmas of fractional calculus, a controller is designed according to the changed fractional chaotic system to synchronize fractional chaotic with nonidentical order in finite time. Numerical simulations are performed to demonstrate the effectiveness of the method.

Hidden Chaotic Attractors and Synchronization for a New Fractional-Order Chaotic System

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Zuoxun Wang ◽  
Jiaxun Liu ◽  
Fangfang Zhang ◽  
Sen Leng
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Chaotic Attractors ◽  
Finite Time Stability ◽  
Integer Order ◽  
Different Types ◽  
Synchronization Scheme

Although a large number of hidden chaotic attractors have been studied in recent years, most studies only refer to integer-order chaotic systems and neglect the relationships among chaotic attractors. In this paper, we first extend LE1 of sprott from integer-order chaotic systems to fractional-order chaotic systems, and we add two constant controllers which could produce a novel fractional-order chaotic system with hidden chaotic attractors. Second, we discuss its complicated dynamic characteristics with the help of projection pictures and bifurcation diagrams. The new fractional-order chaotic system can exhibit self-excited attractor and three different types of hidden attractors. Moreover, based on fractional-order finite time stability theory, we design finite time synchronization scheme of this new system. And combination synchronization of three fractional-order chaotic systems with hidden chaotic attractors is also derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization methods.

Multi-scroll fractional-order chaotic system and finite-time synchronization

2022 ◽  
Author(s):  
Shaohui Yan ◽  
Qiyu Wang ◽  
Ertong Wang ◽  
Xi Sun ◽  
Zhenlong Song
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Secure Communication ◽  
Analog Circuit ◽  
Time Synchronization ◽  
Hidden Attractor ◽  
Initial Values ◽  
Coexistence Of Attractors ◽  
The Time Domain

Abstract The definition of fractional calculus is introduced into the 5D chaotic system, and the 5D fractional-order chaotic system is obtained. The new 5D fractional-order chaotic system has no equilibrium, multi-scroll hidden attractor and multi-stability. By analyzing the time-domain waveform, phase diagram, bifurcation diagram and complexity, it is found that the system has no equilibrium but is very sensitive to parameters and initial values. With the variation of different parameters, the system can produce attractors of different scroll types accompanied by bursting oscillation. Secondly, the multi-stability of the hidden attractor is studied. Different initial values lead to the coexistence of attractors of different scroll number, which shows the advantages of the system. The correctness and realizability of the fractional-order chaotic system are proved by analog circuit and physical implement. Finally, because of the high security of multi-scroll attractor and hidden attractor, finite-time synchronization based on the fractional-order chaotic system is studied, which has a good application prospect in the field of secure communication.

scholarly journals Hidden Coexisting Attractors in a Fractional-Order System without Equilibrium: Analysis, Circuit Implementation, and Finite-Time Synchronization

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Guangchao Zheng ◽  
Ling Liu ◽  
Chongxin Liu
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Secure Communication ◽  
Time Synchronization ◽  
Basins Of Attraction ◽  
Fractional Order System ◽  
Equilibrium Analysis ◽  
Order System ◽  
Coexisting Attractors

In this paper, a novel three-dimensional fractional-order chaotic system without equilibrium, which can present symmetric hidden coexisting chaotic attractors, is proposed. Dynamical characteristics of the fractional-order system are analyzed fully through numerical simulations, mainly including finite-time local Lyapunov exponents, bifurcation diagram, and the basins of attraction. In particular, the system can generate diverse coexisting attractors varying with different orders, which presents ample and complex dynamic characteristics. And there is great potential for secure communication. Then electronic circuit of the fractional-order system is designed to help verify its effectiveness. What is more, taking the disturbances into account, a finite-time synchronization of the fractional-order chaotic system without equilibrium is achieved and the improved controller is proven strictly by applying finite-time stable theorem. Eventually, simulation results verify the validity and rapidness of the proposed method. Therefore, the fractional-order chaotic system with hidden attractors can present better performance for practical applications, such as secure communication and image encryption, which deserve further investigation.

scholarly journals Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Yan Cui ◽  
Hongjun He ◽  
Guan Sun ◽  
Chenhui Lu
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Stability Theory ◽  
Time Synchronization ◽  
Three Dimensional ◽  
Correction Method ◽  
Fractional Order System ◽  
Order System ◽  
Generalized Lorenz System

In this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure. We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. The complexity of fractional order chaotic system is given by spectral entropy algorithm andC0algorithm. We concluded that the fractional order chaotic system has a higher complexity. The fractional order system can generate rich dynamic behavior phenomenon with the values of the parameters and the order changed. We applied the finite time stability theory to design the finite time synchronous controller between drive system and corresponding system. The numerical simulations demonstrate that the controller provides fast and efficient method in the synchronization process.

scholarly journals Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 559 ◽  
Author(s):  
Liang Chen ◽  
Chengdai Huang ◽  
Haidong Liu ◽  
Yonghui Xia
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Unknown Parameters ◽  
Integer Order ◽  
System A ◽  
Control Scheme ◽  
Lorenz Chaotic System

The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.

Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Hadi Delavari ◽  
Danial Senejohnny ◽  
Dumitru Baleanu
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Canonical Form ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Synchronization ◽  
Mode Theory ◽  
Synchronization Scheme

AbstractIn this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.

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