Chaotification of complex networks with impulsive control.

This paper investigates the chaotification problem of complex dynamical networks (CDN) with impulsive control. Both the discrete and continuous cases are studied. The method is presented to drive all states of every node in CDN to chaos. The proposed impulsive control strategy is effective for both the originally stable and unstable CDN. The upper bound of the impulse intervals for originally stable networks is derived. Finally, the effectiveness of the theoretical results is verified by numerical examples.

[1]  W. Ditto,et al.  Controlling chaos in the brain , 1994, Nature.

[2]  Xiang Li,et al.  Chaotifying linear Elman networks , 2002, IEEE Trans. Neural Networks.

[3]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[4]  Xinghuo Yu,et al.  Anticontrol of chaos in continuous-time systems via time-delay feedback. , 2000, Chaos.

[5]  Zhi-Hong Guan,et al.  Chaotification of discrete dynamical systems via impulsive control , 2009 .

[6]  Liu Na,et al.  The Chaotification of Discrete Hopfield Neural Networks via Impulsive Control , 2009 .

[7]  Bing-Hong Wang,et al.  Transition to chaos in small-world dynamical network , 2008 .

[8]  Yeng Chai Soh,et al.  Chaotic cryptosystem with high sensitivity to parameter mismatch , 2003 .

[9]  Jun-an Lu,et al.  Impulsive synchronization of general continuous and discrete-time complex dynamical networks , 2010 .

[10]  Guanrong Chen,et al.  Transition to chaos in complex dynamical networks , 2004 .

[11]  Ramakrishna Ramaswamy,et al.  TARGETING CHAOS THROUGH ADAPTIVE CONTROL , 1998, chao-dyn/9801024.

[12]  Liang Chen,et al.  Controlling bifurcation and Chaos in Internet Congestion Control Model , 2004, Int. J. Bifurc. Chaos.

[13]  Guanrong Chen,et al.  Chaotifying a continuous-time system near a stable limit cycle , 2003 .

[14]  Guanrong Chen,et al.  Bifurcation control of two nonlinear models of cardiac activity , 1997 .

[15]  Feng Zhou,et al.  On impulsive Control and its Application to Chen's Chaotic System , 2002, Int. J. Bifurc. Chaos.

[16]  David J. Hill,et al.  A Hybrid impulsive and Switching Control Strategy for Synchronization of Nonlinear Systems and Application to Chua's Chaotic Circuit , 2006, Int. J. Bifurc. Chaos.

[17]  Zhi-Hong Guan,et al.  Chaotification for a class of cellular neural networks with distributed delays , 2011 .

[18]  W L Ditto,et al.  Controlling neuronal spikes. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Xinchu Fu,et al.  The emergence of chaos in complex dynamical networks , 2006 .

[20]  S. Sinha,et al.  Adaptive control of spatially extended systems: targeting spatiotemporal patterns and chaos , 1998 .

[21]  Ira B. Schwartz,et al.  Dynamics of Large Scale Coupled Structural/ Mechanical Systems: A Singular Perturbation/ Proper Orthogonal Decomposition Approach , 1999, SIAM J. Appl. Math..

[22]  Zhi-Hong Guan,et al.  Generating chaos for discrete time-delayed systems via impulsive control. , 2010, Chaos.

[23]  G. Rangarajan,et al.  Stability of synchronized chaos in coupled dynamical systems , 2002, nlin/0201037.

[24]  Mingzhou Ding,et al.  STABILITY OF SYNCHRONOUS CHAOS AND ON-OFF INTERMITTENCY IN COUPLED MAP LATTICES , 1997 .