Linear control for mixed synchronization of a fractional-order chaotic system

Abstract This paper studies the mixed synchronization of a fractional-order chaotic system. By designing a simple linear controller, anti-phase synchronization of the first two pairs of output signals between the unidirectional systems are realized, and the third pair of signals is complete synchronous. The control scheme is theoretically proven based on final-value theorem of the Laplace transformation, numerical simulations are further provided to verify the feasibility of the theoretical analysis.

[1]  Chunlai Li,et al.  A novel chaotic system and its topological horseshoe , 2013 .

[2]  Jing Zhang,et al.  Amplitude control and projective synchronization of a dynamical system with exponential nonlinearity , 2015 .

[3]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Jiuchao Feng,et al.  Bifurcation Investigation and stability Analysis for Peak Current Mode input-Series output-Parallel DC-DC Converters , 2013, Int. J. Bifurc. Chaos.

[5]  Hongmin Li,et al.  Adaptive impulsive synchronization of a class of chaotic and hyperchaotic systems , 2012 .

[6]  Jürgen Kurths,et al.  SYNCHRONIZATION APPROACH TO ANALYSIS OF BIOLOGICAL SYSTEMS , 2004, The Random and Fluctuating World.

[7]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[8]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[9]  Runtong Chu,et al.  Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice , 2014 .

[10]  Chun-Lai Li,et al.  Adaptive Sliding Mode Control for Synchronization of a Fractional-Order Chaotic System , 2013 .

[11]  Y. Lai,et al.  Observability of lag synchronization of coupled chaotic oscillators. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  P. Butzer,et al.  AN INTRODUCTION TO FRACTIONAL CALCULUS , 2000 .

[13]  Leon O. Chua,et al.  Transmission of Digital signals by Chaotic Synchronization , 1992, Chua's Circuit.

[14]  Jing Zhang,et al.  Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability , 2016, Int. J. Syst. Sci..

[15]  H. Fang,et al.  Feedback control and hybrid projective synchronization of a fractional-order Newton–Leipnik system , 2012 .

[16]  Junqi Yang,et al.  Associated observer-based synchronization for uncertain chaotic systems subject to channel noise and chaos-based secure communication , 2015, Neurocomputing.

[17]  Bo Zhang,et al.  Effects of Couplings on the Collective Dynamics of Permanent-Magnet Synchronous Motors , 2013, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  I. Podlubny.  Fractional differential equations , 1998 .

[19]  Jun-Juh Yan,et al.  Projective synchronization of Chua's chaotic systems with dead-zone in the control input , 2008, Math. Comput. Simul..

[20]  Guochun Xiao,et al.  Bifurcation Analysis in a Digitally Controlled H-Bridge Grid-Connected Inverter , 2014, Int. J. Bifurc. Chaos.

[21]  E. Ahmed,et al.  On fractional order differential equations model for nonlocal epidemics , 2007, Physica A: Statistical Mechanics and its Applications.

[22]  Naser Pariz,et al.  A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter , 2009 .

[23]  Qigui Yang,et al.  Chaos and mixed synchronization of a new fractional-order system with one saddle and two stable node-foci , 2011 .

[24]  Ulrich Parlitz,et al.  Chaotic phase Synchronization Based on Binary Coupling signals , 2000, Int. J. Bifurc. Chaos.

[25]  Arkady Pikovsky,et al.  Synchronization: From pendulum clocks to chaotic lasers and chemical oscillators , 2003 .

[26]  Chun-Lai Li,et al.  Tracking control and generalized projective synchronization of a class of hyperchaotic system with unknown parameter and disturbance , 2012 .

[27]  M. el-Dessoky.  Anti-synchronization of four scroll attractor with fully unknown parameters , 2010 .