scholarly journals LMI-Based Stability of Nonlinear Non-Autonomous Fractional-Order Systems With Multiple Time Delays

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 12016-12026 ◽  
Author(s):  
Shuo Zhang ◽  
Lu Liu ◽  
Xinshu Cui
Keyword(s):  
Fractional Order ◽  
Time Delays ◽  
Multiple Time ◽  
Fractional Order Systems ◽  
Multiple Time Delays

scholarly journals Multi-Switching Combination Synchronization of Three Fractional-Order Delayed Systems

2019 ◽  
Vol 9 (20) ◽  
pp. 4348 ◽  
Author(s):  
Bo Li ◽  
Yun Wang ◽  
Xiaobing Zhou
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Stability Theory ◽  
Time Delays ◽  
Multiple Time ◽  
Fractional Order Systems ◽  
Delayed Systems ◽  
Combination Synchronization ◽  
Multiple Time Delays ◽  
The Stability

Multi-switching combination synchronization of three fractional-order delayed systems is investigated. This is a generalization of previous multi-switching combination synchronization of fractional-order systems by introducing time-delays. Based on the stability theory of linear fractional-order systems with multiple time-delays, we propose appropriate controllers to obtain multi-switching combination synchronization of three non-identical fractional-order delayed systems. In addition, the results of our numerical simulations show that they are in accordance with the theoretical analysis.

scholarly journals Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Li ◽  
Xiaobing Zhou ◽  
Yun Wang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Delays ◽  
Chaotic Systems ◽  
Multiple Time ◽  
Engineering Systems ◽  
Fractional Order Systems ◽  
Combination Synchronization ◽  
Multiple Time Delays ◽  
Practical Engineering

Time delay is a frequently encountered phenomenon in some practical engineering systems and introducing time delay into a system can enrich its dynamic characteristics. There has been a plenty of interesting results on fractional-order chaotic systems or integer-order delayed chaotic systems, but the problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage. Combination synchronization of three different fractional-order delayed chaotic systems is investigated in this paper. It is an extension of combination synchronization of delayed chaotic systems or combination synchronization of fractional-order chaotic systems. With the help of stability theory of linear fractional-order systems with multiple time delays, we design controllers to achieve combination synchronization of three different fractional-order delayed chaotic systems. In addition, numerical simulations have been performed to demonstrate and verify the theoretical analysis.

Influence of multiple time delays on bifurcation of fractional-order neural networks

2019 ◽  
Vol 361 ◽  
pp. 565-582 ◽  
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Ying Guo ◽  
Qimei Xiao ◽  
...  
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Time Delays ◽  
Multiple Time ◽  
Multiple Time Delays

Novel results on projective synchronization of fractional-order neural networks with multiple time delays

2018 ◽  
Vol 117 ◽  
pp. 76-83 ◽  
Author(s):  
Weiwei Zhang ◽  
Jinde Cao ◽  
Ranchao Wu ◽  
Dingyuan Chen ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Time Delays ◽  
Projective Synchronization ◽  
Multiple Time ◽  
Multiple Time Delays

Uniform stability of Fractional Order Leaky Integrator Echo State Neural Network with multiple time delays

2017 ◽  
Vol 418-419 ◽  
pp. 703-716 ◽  
Author(s):  
Seyed Mehdi Abedi Pahnehkolaei ◽  
Alireza Alfi ◽  
J.A. Tenreiro Machado
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Time Delays ◽  
Uniform Stability ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Leaky Integrator

scholarly journals Uniform Stability of a Class of Fractional-Order Nonautonomous Systems with Multiple Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Tao Zou ◽  
Jianfeng Qu ◽  
Yi Chai ◽  
Maoyun Guo ◽  
Congcong Liu
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Time Delays ◽  
Uniform Stability ◽  
Multiple Time ◽  
Uniqueness Of Solutions ◽  
Nonautonomous Systems ◽  
Stability Of Solution ◽  
Multiple Time Delays ◽  
The Stability

In mathematics, to a large extent, control theory addresses the stability of solutions of differential equations, which can describe the behavior of dynamic systems. In this paper, a class of fractional-order nonautonomous systems with multiple time delays modeled by differential equations is considered. A sufficient condition is established for the existence and uniqueness of solutions for such systems involving Caputo fractional derivative, and the uniform stability of solution is studied. At last, two examples are given to demonstrate the applicability of our results.

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