On inverse problem of generalized synchronization between different dimensional integer-order and fractional-order chaotic systems

Chaos is described as a unstable dynamic behavior with dependence on initial conditions. The control and synchronization of chaotic systems requires the knowledge of parameters in advance. Recently researcher's has been shifted from integer order chaotic system to fraction order chaotic system. In this work, based on the stability theory of integer-order linear systems and Lyapunov stability theory, we present some control schemes to achieve a new type of synchronization called inverse generalized synchronization between different dimensional integer and fractional-orders chaotic systems. The effectiveness of the proposed approaches are verified by two numerical examples.

[1]  Djalel Dib,et al.  MPPT control in wind energy conversion systems and the application of fractional control (PIα) in pitch wind turbine , 2016, Int. J. Model. Identif. Control..

[2]  Guodong Wang,et al.  Synchronization of a class of fractional-order and integer order hyperchaotic systems , 2014 .

[3]  Adel Ouannas,et al.  Generalized synchronization of different dimensional chaotic dynamical systems in discrete time , 2015 .

[4]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

[5]  Ahmed M. Soliman,et al.  MOS realization of the double-scroll-like chaotic equation , 2003 .

[6]  Jie Liu,et al.  ANTICIPATING SYNCHRONIZATION OF INTEGER ORDER AND FRACTIONAL ORDER HYPER-CHAOTIC CHEN SYSTEM , 2012 .

[7]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[8]  Mohammed Affan Zidan,et al.  Controllable V-Shape multiscroll Butterfly Attractor: System and Circuit Implementation , 2012, Int. J. Bifurc. Chaos.

[9]  贾立新,et al.  Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems , 2010 .

[10]  张彦斌,et al.  A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system , 2011 .

[11]  Yanping Wu,et al.  Synchronization and Anti-synchronization between a Class of Fractional-order and Integer-order Chaotic Systems with Only One Controller Term , 2022 .

[12]  Shen Ke,et al.  THE CONTROL ACTION OF THE PERIODIC PERTURBATION ON A HYPERCHAOTIC SYSTEM , 1999 .

[13]  Herbert Ho-Ching Iu,et al.  Circuit simulation for synchronization of a fractional-order and integer-order chaotic system , 2013 .

[14]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.

[15]  Adel Ouannas,et al.  On Inverse Generalized Synchronization of Continuous Chaotic Dynamical Systems , 2016 .

[16]  Yan-PingWu,et al.  Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller , 2015 .

[17]  Sundarapandian Vaidyanathan,et al.  Advances in Chaos Theory and Intelligent Control , 2016, Advances in Chaos Theory and Intelligent Control.

[18]  Abdesselem Boulkroune,et al.  Fuzzy Control-Based Function Synchronization of Unknown Chaotic Systems with Dead-Zone Input , 2016, Advances in Chaos Theory and Intelligent Control.

[19]  Moez Feki,et al.  Synchronization of integer order and fractional order Chua's systems using robust observer , 2013, Commun. Nonlinear Sci. Numer. Simul..

[20]  Abdesselem Boulkroune,et al.  Fuzzy adaptive synchronization of uncertain fractional-order chaotic systems , 2016, Int. J. Mach. Learn. Cybern..

[21]  Ahmed Gomaa Radwan,et al.  Stability and non-standard finite difference method of the generalized Chua's circuit , 2011, Comput. Math. Appl..

[22]  A. Azar,et al.  A robust method for new fractional hybrid chaos synchronization , 2017 .

[23]  Ahmed M. Soliman,et al.  An inductorless CMOS realization of Chua’s circuit , 2003 .

[24]  K.N. Salama,et al.  Control and switching synchronization of fractional order chaotic systems using active control technique , 2013, Journal of advanced research.

[25]  A. Radwan,et al.  MOS realization of the modified Lorenz chaotic system , 2004 .

[26]  Ahmed S. Elwakil,et al.  1-d digitally-Controlled multiscroll Chaos Generator , 2007, Int. J. Bifurc. Chaos.

[27]  Qionghua Wang,et al.  A fractional-order hyperchaotic system and its synchronization , 2009 .

[28]  Abdesselem Boulkroune,et al.  Fuzzy Adaptive Synchronization of Uncertain Fractional-Order Chaotic Systems , 2016, Advances in Chaos Theory and Intelligent Control.