General methods for modified projective synchronization of hyperchaotic systems with known or unknown parameters

This work is concerned with the general methods for modified projective synchronization of hyperchaotic systems. A systematic method of active control is developed to synchronize two hyperchaotic systems with known parameters. Moreover, by combining the adaptive control and linear feedback methods, general sufficient conditions for the modified projective synchronization of identical or different chaotic systems with fully unknown or partially unknown parameters are presented. Meanwhile, the speed of parameters identification can be regulated by adjusting adaptive gain matrix. Numerical simulations verify the effectiveness of the proposed methods.

[1]  Zhenya Yan,et al.  Controlling hyperchaos in the new hyperchaotic Chen system , 2005, Appl. Math. Comput..

[2]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

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

[4]  Zhongjun Ma,et al.  Generalized synchronization of different dimensional chaotic dynamical systems , 2007 .

[5]  Liang Chen,et al.  Controlling chaos in an economic model , 2007 .

[6]  Xiaoyun Chen,et al.  Adaptive synchronization of different chaotic systems with fully unknown parameters , 2007 .

[7]  Rong Zhang,et al.  Adaptive full state hybrid projective synchronization of chaotic systems with the same and different order , 2007 .

[8]  Ju H. Park.  Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter , 2007 .

[9]  Zhi-Hong Guan,et al.  Feedback and adaptive control for the synchronization of Chen system via a single variable , 2003 .

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

[11]  Xiaoqun Wu,et al.  Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems , 2005 .

[12]  Guo-Hui Li,et al.  Generalized projective synchronization between two different chaotic systems using active backstepping control , 2006 .

[13]  Liang Chen,et al.  Controlling chaos in Internet congestion control model , 2004 .

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

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

[16]  Rong Zhang,et al.  Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems , 2007 .

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

[18]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[19]  Wei Xu,et al.  Adaptive generalized projective synchronization in different chaotic systems based on parameter identification , 2007 .

[20]  Maritan,et al.  Chaos, noise, and synchronization. , 1994, Physical review letters.

[21]  Young-Jai Park,et al.  Phase synchronization in coupled Nd:YAG lasers , 2001 .

[22]  Xiaofeng Liao,et al.  Impulsive synchronization of nonlinear coupled chaotic systems , 2004 .

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

[24]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[25]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[26]  Guohui Li,et al.  Generalized projective synchronization of two chaotic systems by using active control , 2006 .