Synchronization of a class of fractional-order and integer order hyperchaotic systems

Abstract

In this paper, we bring attention to synchronization between a fractional-order chaotic system and an integer order chaotic system, which is very challenging because it can form a bridge between a fractional-order chaotic system and an integer order chaotic system. More specifically, we present a general form of a class of chaotic system, which can be synchronized between a fractional-order chaotic system and an integer order chaotic system. Furthermore, an example is carried out to verify and demonstrate the effectiveness of the proposed control scheme. Simultaneously, our work is supported by logical theorems and intuitive numerical simulation.

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

“…Proof. By inserting the control law described by (12) into 7, we can rewrite the slave system as follows:…”

“…A sliding mode method has been designed in [9][10][11]. A synchronization method of a class of hyperchaotic systems is given in [12]. In [13], a nonlinear feedback control method has been introduced and some robust observer techniques have been used in [14,15].…”

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

“…A new fuzzy sliding mode method has been proposed in [26], and a sliding mode method has been designed in [27,28]. Synchronization of a class of hyperchaotic systems has been studied in [29]. A practical method, based on circuit simulation, has been presented in [30], and in [31] a robust observer technique has been tackled.…”

Simplified Sliding Mode of a Novel Class of Four-dimensional Fractional-order Chaos

“…In [22], control of a stochastic fractional-order chaos with random and uncertain parameters considered is investigated. In [23], synchronization of a class of integer-order and fractional-order chaos is finished. The dynamic behavior of fractional-order complex Lorenz chaos is analyzed and corresponding control scheme is designed in [24].…”