文档介绍：
Circuit simulation and implementation for synchronization
between fractional-order modified Liu chaotic systems#
MA Tiedong, GUO Dong*
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(College of Automation, Chongqing University, Chongqing 400044)
Abstract: For a novel modified fractional-order Liu chaotic system, this paper studies the circuit
simulation for this system and its synchronization. Based on the approximation theory of
fractional-order operator, an electronic circuit is designed to describe the dynamic behavior of the
modified fractional-order system firstly, and then the synchronization between two identical
fractional-order Liu systems is designed by given circuit. Our results are supported by numerical
simulation and circuit implementation.
Key words: Chaos; Fractional-order Liu system; Synchronization; Circuit simulation
0 Introduction
Recently, the study of fractional differential equations has attracted lots of attention in the past
few decades. In fractional-order version of many famous chaotic system, chaotic attractor are
found, such as Lorenz system [1], Chua system [2], Chen system [3], Lü system [4], Liu system [5],
and so on. It has useful application in many field of science like engineering, physic, mathematical
biology, psychological and life sciences.
Chaos synchronization, another important topic in nonlinear science, has extensive
applications in vast areas of physics and engineering science. Therefore, the synchronization of
fractional-order chaotic systems starts to attract increasing attention due to its potential
applications in munication and control processing [6-8]. During the past two decades, a
variety of approaches which include OGY method [9], linear and nonlinear feedback control [10],
active control [11,12], adaptive control [13] and sliding mode control [14] have been proposed for
synchronization of chaotic systems. Among these synchronization methods, the active control
approach is easy to implement and has de