Chaos synchronization in fractional differential systems

Abstract

This paper presents a brief overview of recent developments in chaos synchronization in coupled fractional differential systems, where the original viewpoints are retained. In addition to complete synchronization, several other extended concepts of synchronization, such as projective synchronization, hybrid projective synchronization, function projective synchronization, generalized synchronization and generalized projective synchronization in fractional differential systems, are reviewed.

Synchronization of fractional-order chaotic systems using unidirectional adaptive full-state linear error feedback coupling

“…From rigorously mathematical theory, some sufficient conditions of global synchronization for linearly coupled chaotic systems are presented in Lü's paper [26]. However, most of their works have a common problem, that is, the chaotic systems they considered must be able to be decomposed into their linear and nonlinear parts independently [21][22][23][24][25]27,32]. Specifically, the n-dimensional chaotic systems must be able to be rewritten in the form of…”

Existence Results for a Nonlocal Coupled System of Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals

“…A delay fractional order model was proposed for the co-infection of malaria and HIV/AIDS in [12]. Chaos synchronization in fractional differential systems was explained in the article [13]. For details on diffusion and reactions in fractals and disordered Systems, we refer the reader to the text [14].…”

On a Coupled System of Fractional Differential Equations with Four Point Integral Boundary Conditions

“…Fractional calculus and more specifically coupled fractional differential equations are amongst the strongest tools of modern mathematics as they play a key role in developing differential models for high complexity systems. Examples include the quantum evolution of complex systems [1], dynamical systems of distributed order [2], chuashirku [3], Duffing system [4], Lorentz system [5], anomalous diffusion [6,7], nonlocal thermoelasticity systems [8,9], secure communication and control processing [10], synchronization of coupled chaotic systems of fractional order [11][12][13][14], etc. In terms of developing high complexity models, applications of coupled fractional differential equations can be significantly extended by dealing with various types of integral boundary conditions.…”