ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

The Adaptive Synchronization of the Stochastic Fractional-order Complex Lorenz System

Journal of Applied Nonlinear Dynamics 4(3) (2015) 267--279 | DOI:10.5890/JAND.2015.09.007

Xiaojun Liu; Ling Hong

State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University Xi’an, 710049, China

Abstract

In this paper, the adaptive synchronization of a stochastic fractionalorder complex Lorenz system is analyzed. Firstly, the Laguerre polynomial approximation method is applied to investigate the fractionalorder system with a random parameter which obeys an exponential distribution. Based on this method, the stochastic system is reduced into the equivalent deterministic one. Besides, based on the stability theory of fractional-order systems, the adaptive synchronization for the deterministic system with unknown parameters is realized by designing appropriate synchronization controllers and estimation laws for uncertain parameters. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.

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