Impulsive complex projective synchronization in drive–response complex coupled dynamical networks

This paper investigates the problem of impulsive complex projective synchronization for drive–response complex-variable dynamical networks with complex coupling, and the dynamical networks with and without delayed complex-variable system nodes are considered. According to the stability analysis of the complex-variable impulsive functional differential equation, the sufficient conditions for achieving complex projective synchronization of drive–response network with complex inner and outer couplings are obtained by taking advantage of the Lyapunov function in the complex fields. In addition, the adaptive coupling strength methods are adopted to achieve the complex projective synchronization. Numerical examples are finally presented to illustrate the effectiveness and correctness of the theoretical results.

[1]  Gang Zhang,et al.  Synchronization of complex dynamical networks via impulsive control. , 2007, Chaos.

[2]  Emad E. Mahmoud,et al.  Chaos synchronization of two different chaotic complex Chen and Lü systems , 2009 .

[3]  Wai Keung Wong,et al.  Impulsive pinning synchronization of stochastic discrete-time networks , 2010, Neurocomputing.

[4]  Jinde Cao,et al.  Anti-periodic solution for delayed cellular neural networks with impulsive effects , 2011 .

[5]  Zhenyuan Xu,et al.  Projective synchronization in drive-response dynamical networks , 2007 .

[6]  Changpin Li,et al.  SYNCHRONIZATION INSIDE COMPLEX DYNAMICAL NETWORKS WITH DOUBLE TIME-DELAYS AND NONLINEAR INNER-COUPLING FUNCTIONS , 2011 .

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

[8]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[9]  Emad E. Mahmoud,et al.  Adaptive anti-lag synchronization of two identical or non-identical hyperchaotic complex nonlinear systems with uncertain parameters , 2012, J. Frankl. Inst..

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

[11]  Shutang Liu,et al.  Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances , 2012 .

[12]  Xinchu Fu,et al.  Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems , 2013 .

[13]  Shuxia Pan,et al.  Propagation of second order integrodifference equations with local monotonicity , 2011 .

[14]  Jin Zhou,et al.  Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization , 2012 .

[15]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[16]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[17]  Xinchu Fu,et al.  Synchronization Of Complex-Variable Dynamical Networks With Complex Coupling , 2013 .

[18]  Jin Zhou,et al.  Synchronization in complex delayed dynamical networks with impulsive effects , 2007 .

[19]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Jinde Cao,et al.  Projective synchronization of a class of delayed chaotic systems via impulsive control , 2009 .

[21]  Song Zheng.  Projective synchronization in a driven-response dynamical network with coupling time-varying delay , 2012 .

[22]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[23]  Guo Liu-Xiao,et al.  Projective Synchronization in Drive--Response Networks via Impulsive Control , 2008 .

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

[25]  Song Zheng.  Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling , 2012 .

[26]  Jitao Sun,et al.  Stability analysis of complex-valued impulsive system , 2013 .

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

[28]  Mark J. McGuinness,et al.  The real and complex Lorenz equations in rotating fluids and lasers , 1982 .

[29]  Xinchu Fu,et al.  Complex projective synchronization in coupled chaotic complex dynamical systems , 2012 .

[30]  Song Zheng,et al.  Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems , 2013 .

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

[32]  F. Garofalo,et al.  Synchronization of complex networks through local adaptive coupling. , 2008, Chaos.

[33]  Emad E. Mahmoud,et al.  Complex complete synchronization of two nonidentical hyperchaotic complex nonlinear systems , 2014 .

[34]  Changpin Li,et al.  Synchronization Analysis of Two Coupled Complex Networks with Time Delays , 2011 .

[35]  Licheng Jiao,et al.  Projective synchronization with different scale factors in a driven–response complex network and its application in image encryption , 2010 .

[36]  Weigang Sun,et al.  Generalized outer synchronization between two uncertain dynamical networks , 2014 .

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