Nonlinear Dynamics

, Volume 65, Issue 4, pp 457–466

Chaos and mixed synchronization of a new fractional-order system with one saddle and two stable node-foci

Original Paper

DOI: 10.1007/s11071-010-9904-2

Cite this article as:
Zeng, C., Yang, Q. & Wang, J. Nonlinear Dyn (2011) 65: 457. doi:10.1007/s11071-010-9904-2


This paper reports a new fractional-order Lorenz-like system with one saddle and two stable node-foci. First, some sufficient conditions for local stability of equilibria are given. Also, this system has a double-scroll chaotic attractor with effective dimension being less than three. The minimum effective dimension for this system is estimated as 2.967. It should be emphasized that the linear differential equation in fractional-order Lorenz-like system seems to be less “sensitive” to the damping, introduced by a fractional derivative, than two other nonlinear equations. Furthermore, mixed synchronization of this system is analyzed with the help of nonlinear feedback control method. The first two pairs of state variables between the interactive systems are anti-phase synchronous, while the third pair of state variables is complete synchronous. Numerical simulations are performed to verify the theoretical results.


Fractional order system Chaos Lorenz-like system Mixed synchronization Minimum effective 

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.School of ScienceSouth China University of TechnologyGuangzhouP.R. China
  2. 2.School of InformaticsGuangdong University of Foreign StudiesGuangzhouP.R. China