Global Mittag-Leffler stability for fractional-order coupled systems on network without strong connectedness

2020 ◽  
Vol 63 (3) ◽  
Author(s):  
Xin Meng ◽  
Yonggui Kao ◽  
Hamid Reza Karimi ◽  
Cunchen Gao
Keyword(s):  
Fractional Order ◽  
Coupled Systems ◽  
Strong Connectedness

Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

2021 ◽  
pp. 014233122110009
Author(s):  
Xin Meng ◽  
Baoping Jiang ◽  
Cunchen Gao
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Coupled Systems ◽  
Projective Synchronization ◽  
Slave System ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Strong Connectedness ◽  
Master System ◽  
Error System

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

Control of amplitude death by coupling range in a network of fractional-order oscillators

2020 ◽  
Vol 34 (31) ◽  
pp. 2050303
Author(s):  
Rui Xiao ◽  
Zhongkui Sun
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Coupling Strength ◽  
Low Frequency ◽  
System Size ◽  
Coupled Systems ◽  
Amplitude Death ◽  
Function Relationship ◽  
The Relationship

We investigate the oscillating dynamics in a ring of network of nonlocally delay-coupled fractional-order Stuart-Landau oscillators. It is concluded that with the increasing of coupling range, the structures of death islands go from richness to simplistic, nevertheless, the area of amplitude death (AD) state is expanded along coupling delay and coupling strength directions. The increased coupling range can prompt the coupled systems with low frequency to occur AD. When system size varies, the area of death islands changes periodically, and the linear function relationship between periodic length and coupling range can be deduced. Thus, one can modulate the oscillating dynamics by adjusting the relationship between coupling range and system size. Furthermore, the results of numerical simulations are consistent with theoretical analysis.

scholarly journals Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Yongjin Li ◽  
Kamal Shah
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Coupled Systems ◽  
Test Problems ◽  
Operational Matrices ◽  
Partial Differential ◽  
Established Technique

We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique.

Analysis of fractional order differential coupled systems

2014 ◽  
Vol 38 (15) ◽  
pp. 3322-3338 ◽  
Author(s):  
JinRong Wang ◽  
Yuruo Zhang
Keyword(s):  
Fractional Order ◽  
Coupled Systems

scholarly journals Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 744 ◽  
Author(s):  
Bei Zhang ◽  
Yonghui Xia ◽  
Lijuan Zhu ◽  
Haidong Liu ◽  
Longfei Gu
Keyword(s):  
Dynamical System ◽  
Graph Theory ◽  
Global Stability ◽  
Fractional Order ◽  
Trivial Solution ◽  
Sufficient Conditions ◽  
Fractional Order System ◽  
Coupled Systems ◽  
Order System ◽  
The Stability

Based on the graph theory and stability theory of dynamical system, this paper studies the stability of the trivial solution of a coupled fractional-order system. Some sufficient conditions are obtained to guarantee the global stability of the trivial solution. Finally, a comparison between fractional-order system and integer-order system ends the paper.

Stabilization of fractional-order coupled systems with time delay on networks

2016 ◽  
Vol 88 (1) ◽  
pp. 521-528 ◽  
Author(s):  
Liping Chen ◽  
Ranchao Wu ◽  
Zhaobi Chu ◽  
Yigang He
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Coupled Systems

scholarly journals Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

2022 ◽  
Vol 27 (1) ◽  
pp. 102-120
Author(s):  
Jin You ◽  
Shurong Sun
Keyword(s):  
Graph Theory ◽  
Control Systems ◽  
Fractional Order ◽  
Impulsive Control ◽  
Coupled Systems ◽  
Practical Stability ◽  
Order System ◽  
Impulsive Control Systems ◽  
New Criteria ◽  
Noninstantaneous Impulses

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results

Sign in / Sign up

Export Citation Format

Share Document