scholarly journals Bifurcations and Synchronization of the Fractional-Order Bloch System

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Honggang Dang ◽  
Lixin Yang
Keyword(s):  
Fractional Order ◽  
Limit Cycles ◽  
System Parameter ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
Unknown Parameters ◽  
The Rich ◽  
Period Limit ◽  
The Stability

In this paper, bifurcations and synchronization of a fractional-order Bloch system are studied. Firstly, the bifurcations with the variation of every order and the system parameter for the system are discussed. The rich dynamics in the fractional-order Bloch system including chaos, period, limit cycles, period-doubling, and tangent bifurcations are found. Furthermore, based on the stability theory of fractional-order systems, the adaptive synchronization for the system with unknown parameters is realized by designing appropriate controllers. Numerical simulations are carried out to demonstrate the effectiveness and flexibility of the controllers.

CHAOS AND ADAPTIVE SYNCHRONIZATIONS IN FRACTIONAL-ORDER SYSTEMS

2013 ◽  
Vol 23 (11) ◽  
pp. 1350175 ◽  
Author(s):  
XIAOJUN LIU ◽  
LING HONG
Keyword(s):  
Fractional Order ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
Effective Dimension ◽  
Unknown Parameters ◽  
Order Case ◽  
The Stability ◽  
Fifth Order ◽  
Derivative Order

In this paper, chaos and adaptive synchronization for a fractional-order Genesio–Tesi system with fifth order nonlinearity are investigated. The minimum effective dimension for the system to remain chaotic is 2.784 in the commensurate-order case and 2.793 in the incommensurate-order case. A period-doubling bifurcation and an interior crisis from single-scroll to double-scroll attractors are also found with the variation of derivative order. Furthermore, based on the stability theory of fractional-order systems, the adaptive synchronization of the system with unknown parameters is realized by designing appropriated controllers. Numerical simulations are carried out to demonstrate the effectiveness and flexibility of the controllers.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

Adaptive Synchronization of Fractional Hyper-Chaotic System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 868-871 ◽  
Author(s):  
Li Xin Yang ◽  
Wan Sheng He ◽  
Jin Ping Jia ◽  
Fan Di Zhang
Keyword(s):  
Fractional Order ◽  
Tracking Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Fractional Systems ◽  
Control Approach ◽  
The Stability

In this paper, chaos synchronization of the modified Sprott E system is investigated. Based on the stability theorem for fractional systems, tracking control approach is used for the fractional-order systems with uncertain parameters. Meanwhile, suitable adaptive synchronization controller and recognizing rules of the uncertain parameters are designed. Numerical simulation results show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order hyper-chaotic systems.

Adaptive Synchronization of a Fractional-Order Complex T System With a Random Parameter

2015 ◽  
Author(s):  
Xiaojun Liu ◽  
Ling Hong
Keyword(s):  
Fractional Order ◽  
Laguerre Polynomial ◽  
Random Parameter ◽  
Adaptive Synchronization ◽  
Order System ◽  
Deterministic System ◽  
Order Complex ◽  
Unknown Parameters ◽  
The Stability ◽  
T System

In this paper, the adaptive synchronization of a fractional-order complex T system with a random parameter is analyzed. Firstly, the Laguerre polynomial approximation method is applied to investigate the fractional-order system with a random parameter which obeys an exponential distribution. Based on this method, the stochastic system is reduced into the equivalent deterministic one. The improved Adams-Bashforth-Moulton algorithm with the predictor-correctors scheme is used to solve the approximately deterministic system numerically. Based on the stability theory of fractional-order systems, the synchronization for the deterministic system with unknown parameters is realized by designing appropriate synchronization controllers and estimation law for uncertain parameters. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.

Synchronization of a Fractional-Order System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 796-799
Author(s):  
Xiao Ya Yang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
Unknown Parameters ◽  
The Stability

In this paper, synchronization of a fractional-order system with unknown parameters is studied. The chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, suitable synchronization controllers and parameter identification rules for the unknown parameters are designed. Numerical simulations are used to demonstrate the effectiveness of the controllers.

scholarly journals The Dynamics and Synchronization of a Fractional-Order System with Complex Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaoya Yang ◽  
Xiaojun Liu ◽  
Honggang Dang ◽  
Wansheng He
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Complex Variables ◽  
Fractional Order System ◽  
Order System ◽  
Chaotic Attractors ◽  
Fractional Order Systems ◽  
System Parameters ◽  
The Stability

A fractional-order system with complex variables is proposed. Firstly, the dynamics of the system including symmetry, equilibrium points, chaotic attractors, and bifurcations with variation of system parameters and derivative order are studied. The routes leading to chaos including the period-doubling and tangent bifurcations are obtained. Then, based on the stability theory of fractional-order systems, the scheme of synchronization for the fractional-order complex system is presented. By designing appropriate controllers, the synchronization for the system is realized. Numerical simulations are carried out to demonstrate the effectiveness of the proposed scheme.

Adaptive Synchronization of the Fractional-Order Sprott N System

2013 ◽  
Vol 850-851 ◽  
pp. 872-875
Author(s):  
Hong Gang Dang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Phase Plane ◽  
Adaptive Synchronization ◽  
Chaotic Attractors ◽  
Fractional Order Systems ◽  
The Stability

In this paper, adaptive synchronization of the fractional-order Sprott N system is investigated. Firstly, the chaotic attractors on different phase plane of the system are got by means of numerical simulation. Then based on the stability theory of fractional-order systems, the adaptive synchronization of the system is realized. Numerical simulations are used to demonstrate the effectiveness for the controllers.

scholarly journals Adaptive Synchronization of Fractional-Order Complex-Valued Chaotic Neural Networks with Time-Delay and Unknown Parameters

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 924-941
Author(s):  
Mei Li ◽  
Ruoxun Zhang ◽  
Shiping Yang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Adaptive Synchronization ◽  
Order Complex ◽  
Unknown Parameters ◽  
Chaotic Neural Networks ◽  
Controlled Systems ◽  
The Stability ◽  
Complex Valued

The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. Synchronization between a driving FOCVCNN and a response FOCVCNN, as well as the identification of unknown parameters are implemented. Based on fractional complex-valued inequalities and stability theory of fractional-order chaotic complex-valued systems, the paper designs suitable adaptive controllers and complex update laws. Moreover, it scientifically estimates the uncertainties and external disturbances to establish the stability of controlled systems. The computer simulation results verify the correctness of the proposed method. Not only a new method for analyzing FOCVCNNs with time-delay and unknown complex parameters is provided, but also a sensitive decrease of the computational and analytical complexity.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

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