Chaos synchronization of fractional order financial systems with time-delay based on sliding control

2014 ◽  
Vol 31 (6) ◽  
pp. 626 ◽  
Author(s):  
Tao Zhu ◽  
Guangjun Zhang ◽  
Hong Yao ◽  
Rui Li
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Financial Systems ◽  
Sliding Control

scholarly journals Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jianeng Tang
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Technique ◽  
The Laplace Transform

Chaos synchronization of different fractional order time-delay chaotic systems is considered. Based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method. At last, effects of the fraction order and the time delay on synchronization are further researched.

scholarly journals Results for Chaos Synchronization with New Multi-Fractional Order of Neural Networks by Multi-Time Delay

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Fatin Nabila Abd Latiff ◽  
Wan Ainun Mior Othman
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Direct Method ◽  
Extensive Literature ◽  
Control Scheme ◽  
New Finding

A new finding is proposed for multi-fractional order of neural networks by multi-time delay (MFNNMD) to obtain stable chaotic synchronization. Moreover, our new result proved that chaos synchronization of two MFNNMDs could occur with fixed parameters and initial conditions with the proposed control scheme called sliding mode control (SMC) based on the time-delay chaotic systems. In comparison, the fractional-order Lyapunov direct method (FLDM) is proposed and is implemented to SMC to maintain the systems’ sturdiness and assure the global convergence of the error dynamics. An extensive literature survey has been conducted, and we found that many researchers focus only on fractional order of neural networks (FNNs) without delay in different systems. Furthermore, the proposed method has been tested with different multi-fractional orders and time-delay values to find the most stable MFNNMD. Finally, numerical simulations are presented by taking two MFNNMDs as an example to confirm the effectiveness of our control scheme.

scholarly journals Trajectory tracking error using fractional order time-delay recurrent neural networks using Krasovskii-Lur’e functional for Chua’s circuit via inverse optimal control

2019 ◽  
Vol 66 (1) ◽  
pp. 98
Author(s):  
J. Perez Padrón ◽  
J.P. Pérez Padrón ◽  
C.F. Mendez-Barrios ◽  
E.J. Gonzalez-Galvan
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Optimal Control ◽  
Time Delay ◽  
Fractional Order ◽  
Trajectory Tracking ◽  
Recurrent Neural Networks ◽  
Chaos Synchronization ◽  
Tracking Error ◽  
Inverse Optimal Control

This paper presents an application of a Fractional Order Time Delay Neural Networks to chaos synchronization. The two main methodologies, on which the approach is based, are fractional order time-delay recurrent neural networks and the fractional order  inverse optimal control for nonlinear systems. The problem of trajectory tracking is studied, based on the fractional order Lyapunov-Krasovskii and Lur’e theory, that achieves the global asymptotic stability of the tracking error between a delayed recurrent neural network and a reference function is obtained. The method is illustrated for the synchronization, the analytic results we present a trajectory tracking simulation of a fractional order time-delay dynamical network and the Fractional Order Chua’s circuits

scholarly journals Adaptive Predefined-Time Synchronization of Two Different Fractional-Order Chaotic Systems With Time-Delay

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 31908-31920
Author(s):  
Lixiong Lin ◽  
Qing Wang ◽  
Bingwei He ◽  
Yanjie Chen ◽  
Xiafu Peng ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Time Synchronization
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