Module-phase synchronization in hyperchaotic complex Lorenz system after modified complex projection

Abstract This paper studies the modified complex projective synchronization which has plural projective factors and is meaningful to complex systems, and applies this kind of synchronization in a hyperchaotic complex Lorenz system. Based on the proposed synchronization, we also study the hybrid synchronization which contains modified complex projection and module-phase synchronization because hybrid synchronization not only deal with the synchronization real part and imaginary part, respectively, but also take module and phase of complex system into consideration. Owing to it is difficult to design the controller directly, our work involve an intermediary system. The asymptotic convergence of the errors between the states is proven and the computer simulation results present the effectiveness of our method.

[1]  Julien Clinton Sprott,et al.  Controlling chaos in a high dimensional system with periodic parametric perturbations , 1999 .

[2]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[3]  Giuseppe Grassi,et al.  Synchronizing chaotic systems up to an arbitrary scaling matrix via a single signal , 2012, Appl. Math. Comput..

[4]  Tao Wang,et al.  Chaos control and hybrid projective synchronization of several new chaotic systems , 2012, Appl. Math. Comput..

[5]  Tiedong Ma,et al.  On the exponential synchronization of stochastic impulsive chaotic delayed neural networks , 2011, Neurocomputing.

[6]  Huaguang Zhang,et al.  Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Ming-Chung Ho,et al.  Phase and anti-phase synchronization of two chaotic systems by using active control , 2002 .

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

[9]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[10]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[11]  Guanrong Chen,et al.  On area-preserving non-hyperbolic chaotic maps: A case study , 2003 .

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

[13]  Gaogao Dong,et al.  A new hyperchaotic system and its synchronization , 2010, Appl. Math. Comput..

[14]  Rui-hong Li,et al.  A special full-state hybrid projective synchronization in symmetrical chaotic systems , 2008, Appl. Math. Comput..

[15]  Ma Tie-Dong,et al.  An improved impulsive control approach to robust lag synchronization between two different chaotic systems , 2010 .

[16]  Da Lin,et al.  Module-phase synchronization in complex dynamic system , 2010, Appl. Math. Comput..

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

[18]  G. Mahmoud,et al.  Lag synchronization of hyperchaotic complex nonlinear systems , 2012 .

[19]  Huaguang Zhang,et al.  On passivity analysis for stochastic neural networks with interval time-varying delay , 2010, Neurocomputing.

[20]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

[21]  S. Codreanu.  Synchronization of spatiotemporal nonlinear dynamical systems by an active control , 2003 .

[22]  Tiedong Ma,et al.  Delay-probability-distribution-dependent robust stability analysis for stochastic neural networks with time-varying delay , 2009 .

[23]  J. M. Gonzalez-Miranda,et al.  Generalized synchronization in directionally coupled systems with identical individual dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.