Adaptive modified function projective synchronization of unknown chaotic systems with different order

Abstract This paper investigates the modified function projective synchronization (MFPS) between two different dimensional chaotic systems with fully unknown or partially unknown parameters via increased order. Based on the Lyapunov stability theorem and adaptive control method, a unified adaptive controller and parameters update law can be designed for achieving the MFPS of the two different chaotic systems with different orders. Numerical simulations are presented to show the effectiveness of the proposed synchronization scheme.

[1]  Zheng Song,et al.  Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system , 2008 .

[2]  Debin Huang.  Synchronization-based estimation of all parameters of chaotic systems from time series. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Luo Runzi,et al.  Adaptive function project synchronization of Rössler hyperchaotic system with uncertain parameters , 2008 .

[4]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[5]  Zuolei Wang,et al.  Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters , 2009 .

[6]  Z. Guan,et al.  Generalized synchronization of continuous chaotic system , 2006 .

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

[8]  Zuolei Wang.  Projective synchronization of hyperchaotic Lü system and Liu system , 2010 .

[9]  Ming-Chung Ho,et al.  Reduced-order synchronization of chaotic systems with parameters unknown , 2006 .

[10]  Jinde Cao,et al.  Parameter identification of dynamical systems from time series. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Tian Li-xin,et al.  A new hyperchaotic system and its linear feedback control , 2008 .

[12]  Hongyue Du,et al.  Modified function projective synchronization of chaotic system , 2009 .

[13]  Yuxiang Chen,et al.  Lag synchronization of structurally nonequivalent chaotic systems with time delays , 2007 .

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

[15]  H. N. Agiza,et al.  Chaos synchronization of Lü dynamical system , 2004 .

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

[17]  Wei Lin,et al.  Failure of parameter identification based on adaptive synchronization techniques. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  M. Noorani,et al.  Adaptive anti-synchronization of two identical and different hyperchaotic systems with uncertain parameters , 2010 .

[19]  Hongyue Du,et al.  Function projective synchronization of different chaotic systems with uncertain parameters , 2008 .

[20]  Guohui Li.  Modified projective synchronization of chaotic system , 2007 .

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

[22]  R. Konnur.  Synchronization-based approach for estimating all model parameters of chaotic systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Gang Feng,et al.  Parameter identification based synchronization for a class of chaotic systems with offset vectors , 2004 .

[24]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[25]  Terrence J. Sejnowski,et al.  Cooperative behavior of a chain of synaptically coupled chaotic neurons , 1998 .