Impulsive Synchronization for a New Chaotic oscillator

Synchronization for a new proposed chaotic system based on impulsive control theory is presented. This new chaotic oscillator is a third order polynomial system (Jerk system), which was developed after the addition of a third state and innovation terms to the well known second order Van der Pol oscillator. The chaotic behavior of this new system is confirmed by using Lyapunov exponents, Poincare maps, Fourier spectrum analysis and numerical experiments. Impulsive synchronization is achieved using just one channel of communication.

[1]  T. Saito,et al.  An RC OTA hysteresis chaos generator , 1996, 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96.

[2]  J. C. Sprotta.  Simple chaotic systems and circuits , 2000 .

[3]  Chen Guan.  CHAOS CONTROL AND ANTI-CONTROL , 2002 .

[4]  Leonardo Acho Zuppa,et al.  A chaotic oscillator using the Van der Pol dynamic immersed into a Jerk system , 2003 .

[5]  Ahmed S. Elwakil,et al.  Creation of a complex butterfly attractor using a novel Lorenz-Type system , 2002 .

[6]  Leon O. Chua,et al.  Experimental Results of Impulsive Synchronization Between Two Chua's Circuits , 1998 .

[7]  John Guckenheimer,et al.  The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations , 2003, SIAM J. Appl. Dyn. Syst..

[8]  Xinzhi Liu,et al.  Application of Impulsive Synchronization to Communication Security , 2003 .

[9]  Guanrong Chen,et al.  Chaotifying a stable LTI system by tiny feedback control , 2000 .

[10]  Hilaire Bertrand Fotsin,et al.  Analog simulation of the dynamics of a van der Pol oscillator coupled to a Duffing oscillator , 2001 .

[11]  Guanrong Chen.  Control and anticontrol of chaos , 1997, 1997 1st International Conference, Control of Oscillations and Chaos Proceedings (Cat. No.97TH8329).

[12]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[13]  Julien Clinton Sprott,et al.  Simple chaotic systems and circuits , 2000 .

[14]  Julien Clinton Sprott,et al.  Algebraically Simple Chaotic Flows , 2000 .

[15]  Mao-Yin Chen,et al.  An Iteration Method for Chaotifying and Controlling Dynamical Systems , 2002, Int. J. Bifurc. Chaos.

[16]  D. W. Moore,et al.  A Thermally Excited Non-Linear Oscillator , 1966 .

[17]  Tao Yang,et al.  Impulsive control , 1999, IEEE Trans. Autom. Control..

[18]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[19]  Julien Clinton Sprott,et al.  A new class of chaotic circuit , 2000 .

[20]  Qidi Wu,et al.  Impulsive control for the stabilization and synchronization of Lorenz systems , 2002 .

[21]  Y. Soh,et al.  The stabilization and synchronization of Chua's oscillators via impulsive control , 2001 .

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

[23]  Chaos of the relativistic parametrically forced van der Pol oscillator , 1997, chao-dyn/9710010.

[24]  Xinzhi Liu,et al.  Robust impulsive synchronization of uncertain dynamical networks , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.