Modified projective synchronization and control of complex Chen and Lü systems

In this paper we present a modified projective synchronization of complex Chen and Lü systems which were introduced recently in our work. These complex systems appear in many important fields of physics and engineering, for example, laser physics, nonlinear circuits and secure communication. The active control technique based on a Lyapunov function is used to synchronize the chaotic attractors of both identical and different systems. Controlling these attractors is investigated by adding a complex periodic forcing. The control performances are verified by calculating Lyapunov exponents. Numerical computations are presented to verify our analytical results for control functions to achieve the modified projective synchronization.

[1]  Mark J. McGuinness,et al.  The real and complex Lorenz equations and their relevance to physical systems , 1983 .

[2]  Xingyuan Wang,et al.  Nonlinear observer based phase synchronization of chaotic systems , 2007 .

[3]  Fausto Cattaneo,et al.  Nonlinear dynamos: A complex generalization of the Lorenz equations , 1985 .

[4]  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.

[5]  Q. Jia.  Projective synchronization of a new hyperchaotic Lorenz system , 2007 .

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

[7]  T. Bountis,et al.  Dynamical properties and synchronization of complex non-linear equations for detuned lasers , 2009 .

[8]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[9]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[10]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[11]  Mark Hess,et al.  TRANSITION TO PHASE SYNCHRONIZATION OF CHAOS , 1998 .

[12]  Young-Jai Park,et al.  Anti-synchronization of chaotic oscillators , 2003 .

[13]  Chuandong Li,et al.  Anti-Synchronization of a Class of Coupled Chaotic Systems via Linear Feedback Control , 2006, Int. J. Bifurc. Chaos.

[14]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[15]  Gamal M. Mahmoud,et al.  BASIC PROPERTIES AND CHAOTIC SYNCHRONIZATION OF COMPLEX LORENZ SYSTEM , 2007 .

[16]  Gamal M. Mahmoud,et al.  Chaotic and hyperchaotic attractors of a complex nonlinear system , 2008 .

[17]  Jian-an Fang,et al.  General methods for modified projective synchronization of hyperchaotic systems with known or unknown parameters , 2008 .

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

[19]  Gamal M. Mahmoud,et al.  Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system , 2007 .

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

[21]  Tassos Bountis,et al.  The Dynamics of Systems of Complex Nonlinear oscillators: a Review , 2004, Int. J. Bifurc. Chaos.

[22]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[23]  Chuandong Li,et al.  Lag synchronization of hyperchaos with application to secure communications , 2005 .

[24]  Shihua Chen,et al.  Lag synchronizing chaotic system based on a single controller , 2008 .

[25]  N. Abraham,et al.  Global stability properties of the complex Lorenz model , 1996 .

[26]  Peng,et al.  Synchronizing hyperchaos with a scalar transmitted signal. , 1996, Physical review letters.

[27]  Yinping Zhang,et al.  Chaotic synchronization and anti-synchronization based on suitable separation , 2004 .