scholarly journals Dynamic Analysis of Complex Synchronization Schemes between Integer Order and Fractional Order Chaotic Systems with Different Dimensions

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Adel Ouannas ◽  
Xiong Wang ◽  
Viet-Thanh Pham ◽  
Toufik Ziar
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Effective Control ◽  
Lyapunov Approach ◽  
Integer Order ◽  
Fractional Order Differential Equations ◽  
Control Schemes ◽  
Stability Method ◽  
Different Dimensions ◽  
Theoretical Results

We present new approaches to synchronize different dimensional master and slave systems described by integer order and fractional order differential equations. Based on fractional order Lyapunov approach and integer order Lyapunov stability method, effective control schemes to rigorously study the coexistence of some synchronization types between integer order and fractional order chaotic systems with different dimensions are introduced. Numerical examples are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.

scholarly journals A Robust Control Method forQ-SSynchronization between Different Dimensional Integer-Order and Fractional-Order Chaotic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Adel Ouannas ◽  
Raghib Abu-Saris
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Approach ◽  
Integer Order ◽  
Control Scheme ◽  
Master System ◽  
Different Dimensions ◽  
Hyperchaotic Systems

A robust control approach is presented to study the problem ofQ-Ssynchronization between Integer-order and fractional-order chaotic systems with different dimensions. Based on Laplace transformation and stability theory of linear integer-order dynamical systems, a new control law is proposed to guarantee theQ-Ssynchronization betweenn-dimensional integer-order master system andm-dimensional fractional-order slave system. This paper provides further contribution to the topic ofQ-Schaos synchronization between integer-order and fractional-order systems and introduces a general control scheme that can be applied to wide classes of chaotic and hyperchaotic systems. Illustrative example and numerical simulations are used to show the effectiveness of the proposed method.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals Consensus of Fractional-Order Multiagent Systems with Nonuniform Time Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jun Liu ◽  
Kaiyu Qin ◽  
Wei Chen ◽  
Ping Li ◽  
Mengji Shi
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
External Environment ◽  
Domain Theory ◽  
Dynamical Model ◽  
Integer Order ◽  
The Laplace Transform ◽  
Simulation Results ◽  
Theoretical Results

Due to the complex external environment, many multiagent systems cannot be precisely described or even cannot be described by an integer-order dynamical model and can only be described by a fractional-order dynamical model. In this paper, consensus problems are investigated for two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: FOMAS with symmetric time delays and undirected topology and FOMAS with asymmetric time delays and directed topology. Employing the Laplace transform and the frequency-domain theory, two delay margins are obtained to guarantee the consensus for the two types of FOMAS, respectively. These results are also suitable for the integer-order dynamical model. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.

scholarly journals Compound Difference Anti-Synchronization between Hyper-Chaotic Systems of Fractional Order

2020 ◽  
Vol 12 (2) ◽  
pp. 175-181 ◽  
Author(s):  
A. Khan ◽  
L. S. Jahanzaib ◽  
Nasreen ◽  
P. Trikha ◽  
T. Khan
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Theoretical Results

In this article, the compound difference anti-synchronization between fractional order hyper-chaotic systems have been studied. Numerical simulations have been performed using MATLAB to verify the theoretical results on fractional order Xling, Vanderpol, Rikitake and Rabinovich hyper-chaotic systems.

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