[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
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)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

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

Download Full Text PDF

 

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.

References

  1. [1]  Li, C.P., Deng, W.H and Xu, D. (2006) Chaos synchronization of the chua system with a fractional order. Physica A, 360, 171-185.
  2. [2]  Ge, Z.M. and Ou, C.Y. (2005) Chaos in a fractional order modified duffing system. In: Proc ECCTD. Budapest, 1259-1262.
  3. [3]  Lu, J.G. and Chen, G.R. (2006) A note on the fractional-order chen system. Chaos Solitons & Fractals, 27, 685-688.
  4. [4]  Ma, S.J., Xu, W. and Fang, T. (2008) Analysis of period-doubling bifurcation in double-well stochastic duffing system via laguerre polynomial approximation. Nonlinear Dynamics,52, 289-299.
  5. [5]  Ma, S.J., Shen, Q. and Hou, J. (2013) Modified projective synchronization of stochastic fractional order chaotic systems with uncertain parameters. Nonlinear Dynamics, 73, 93-100.
  6. [6]  Tavazoei, M. S. and Haeri, M. (2007) A necessary condition for double scroll attractor existence in fractionalorder systems. Physics Letters A, 367, 102-113.
  7. [7]  Jia, H.Y. Chen, Z.Q and W. Xue. (2013) Analysis and circuit mplementation for the fractional-order lorenz system., ACTA PHYSICA SINICA, 62, 140503.
  8. [8]  Moghtadaei, M. and Hashemi Golpayegani, M.R. (2012) Complex dynamic behaviors of the complex lorenz system. Scientia Iranica, 19, 733-738.
  9. [9]  Wang, X.Y. and Zhang, H. (2013) Bivariate module-phase synchronization of a fractional-order lorenz system in different dimensions. Journal of Computation and Nonlinear Dynamics, 8, 031017.
  10. [10]  Luo, C. and Wang, X.Y. (2013) Chaos in the fractional-order complex lorenz system and its synchronization. Nonlinear dynamics, 71, 241-257.
  11. [11]  Diethelm,K., Ford, N.J. and Freed, A.D. (2002), A predictor-corrector approach for the numerical solution of fractional diffrential equations. Nonlinear Dynamics, 29, 3-22.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates