Synchronisation of the hyperchaotic complex Lorenz system in a finite time

In this paper, we investigate the finite-time chaos synchronisation of hyperchaotic complex Lorenz systems. The sufficient conditions for achieving the finite-time synchronisation of two chaotic systems are derived based on the theory of finite-time stability of dynamical systems. In fact, we propose a simple adaptive control method for realising chaos synchronisation in a finite time. It is shown that the technique introduced here can be further applied to various finite-time synchronisations between dynamical systems. Simulation results show the effectiveness of the proposed method.

[1]  Ju H. Park.  On synchronization of unified chaotic systems via nonlinear Control , 2005 .

[2]  Robert A. Van Gorder,et al.  The chaotic Dadras-Momeni system: control and hyperchaotification , 2016, IMA J. Math. Control. Inf..

[3]  Nikolay V. Kuznetsov,et al.  On differences and similarities in the analysis of Lorenz, Chen, and Lu systems , 2014, Appl. Math. Comput..

[4]  Hideo Makino,et al.  Synchronization with low power consumption of hardware models of cardiac cells. , 2005, Bio Systems.

[5]  Gennady A. Leonov,et al.  Non-local methods for pendulum-like feedback systems , 1992 .

[6]  Mark J. McGuinness,et al.  The complex Lorenz equations , 1982 .

[7]  Wei Zhang,et al.  Finite-time chaos synchronization of unified chaotic system with uncertain parameters , 2009 .

[8]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[9]  S. Effati,et al.  Optimal and adaptive control for a kind of 3D chaotic and 4D hyper-chaotic systems , 2014 .

[10]  Sohrab Effati,et al.  New ultimate bound sets and exponential finite-time synchronization for the complex Lorenz system , 2015, J. Complex..

[11]  Shuang Li,et al.  Finite-time stabilization for hyper-chaotic Lorenz system families via adaptive control , 2013 .

[12]  Euntai Kim,et al.  Fuzzy model based adaptive synchronization of uncertain chaotic systems: Robust tracking control approach , 2009 .

[13]  Chunjiang Qian,et al.  Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems , 2006, IEEE Transactions on Automatic Control.

[14]  C. P. Unsworth,et al.  Fast synchronisation of chaotic maps for secure chaotic communications , 2010 .

[15]  Lan Chen,et al.  Experimental study of chaos synchronization in the Belousov–Zhabotinsky chemical system , 2004 .

[16]  Yang Li,et al.  Lag synchronisation of chaotic systems using sliding mode control , 2014, Int. J. Model. Identif. Control..

[17]  Kangsheng Chen,et al.  Experimental study on tracking the state of analog Chua's circuit with particle filter for chaos synchronization , 2008 .

[18]  Sundarapandian Vaidyanathan.  Generalised projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control , 2014, Int. J. Model. Identif. Control..

[19]  Emad E. Mahmoud,et al.  ANALYSIS OF HYPERCHAOTIC COMPLEX LORENZ SYSTEMS , 2008 .

[20]  Leonid M. Fridman,et al.  Decentralised control for complex systems - an invited survey , 2014, Int. J. Model. Identif. Control..

[21]  Tassos Bountis,et al.  Active Control and Global Synchronization of the Complex Chen and lÜ Systems , 2007, Int. J. Bifurc. Chaos.

[22]  U. Vincent,et al.  Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller , 2011 .

[23]  Sohrab Effati,et al.  Ultimate bound sets of a hyperchaotic system and its application in chaos synchronization , 2015, Complex..

[24]  Liang Wu,et al.  Coexistence and switching of anticipating synchronization and lag synchronization in an optical system , 2003 .

[25]  H. Haken,et al.  Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[26]  Wei Lin,et al.  Global finite-time stabilization of a class of uncertain nonlinear systems , 2005, Autom..

[27]  Wenguang Yu.  Finite-time stabilization of three-dimensional chaotic systems based on CLF , 2010 .

[28]  Sundarapandian Vaidyanathan.  Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities , 2014, Int. J. Model. Identif. Control..

[29]  Emad E. Mahmoud,et al.  On the hyperchaotic complex Lü system , 2009 .

[30]  Sundarapandian Vaidyanathan,et al.  Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system , 2015, Int. J. Model. Identif. Control..

[31]  Xiaofeng Wu,et al.  Global finite-time synchronization of a class of the non-autonomous chaotic systems , 2012 .

[32]  Mohammad Pourmahmood Aghababa,et al.  Finite-time stabilization of a non-autonomous chaotic rotating mechanical system , 2012, J. Frankl. Inst..