Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control

The model and the normalized state equations of the novel version of the Colpitts oscillator designed to operate in the ultra-high frequency range are presented. The circuit is investigated numerically and simulations demonstrate chaos in the microwave frequency range. Typical phase portrait, Lyapunov exponent and Lyapunov dimension are calculated using a piece-wise linear approximation of nonlinear I–V characteristic of the bipolar junction transistor. In addition, the feedback controller is applied to achieve chaos synchronization for two identical improved chaotic Colpitts oscillators. In the frame the nonlinear function of the system is used as a nonlinear feedback term for the stability of the error dynamics. Finally, numerical simulations show that this control method is feasible for this oscillator.

[1]  J. Yorke,et al.  The liapunov dimension of strange attractors , 1983 .

[2]  Jamal Daafouz,et al.  Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification , 2005 .

[3]  C. Wegener.  RF chaotic Colpitts oscillator , 1995 .

[4]  G. M. Maggio,et al.  Classification of steady-state behavior of the Colpitts oscillator , 1999, ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357).

[5]  A. Tamasevicius,et al.  Synchronization of VHF chaotic Colpitts oscillators , 2001 .

[6]  张超,et al.  Synchronization between two different chaotic systems with nonlinear feedback control , 2007 .

[7]  A. I. Panas,et al.  Wideband microwave chaotic oscillators , 2002, ICCSC'02. 1st IEEE International Conference on Circuits and Systems for Communications. Proceedings (IEEE Cat. No.02EX605).

[8]  姜璐,et al.  Some new exact solutions to the Burgers–Fisher equation and generalized Burgers–Fisher equation , 2007 .

[9]  A. Tamasevicius,et al.  Improved chaotic Colpitts oscillator for ultrahigh frequencies , 2004 .

[10]  Antanas Cenys,et al.  Two-stage chaotic Colpitts oscillator , 2001 .

[11]  L. X. Ran,et al.  Microwave Chaotic Colpitts Oscillator: Design, Implementation and Applications , 2006 .

[12]  G. Mykolaitis,et al.  Chaotic Colpitts Oscillator for the Ultrahigh Frequency Range , 2006 .

[13]  T. Jiang,et al.  A NEW ARCHITECTURE OF UWB RADAR UTILIZING MICROWAVE CHAOTIC SIGNALS AND CHAOS SYNCHRONIZATION , 2007 .

[14]  K. Giannakopoulos,et al.  A comparison of five methods for studying a hyperchaotic circuit , 2005 .

[15]  G. Mykolaitis,et al.  Numerical Investigation and Experimental Demonstration of Chaos from Two-Stage Colpitts Oscillator in the Ultrahigh Frequency Range , 2006 .

[16]  Moez Feki,et al.  Observer-based chaotic synchronization in the presence of unknown inputs , 2003 .

[17]  J. M. Ngundam,et al.  Synchronization of Colpitts oscillators with different orders , 2009 .

[18]  Gytis Mykolaitis,et al.  Two-stage chaotic Colpitts oscillator for the UHF range , 2004 .

[19]  Michael Peter Kennedy.  Chaos in the Colpitts oscillator , 1994 .

[20]  R. Ostojic,et al.  Synchronization of chaotic Colpitts oscillators with applications to binary communications , 1999, ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357).

[21]  Michael Peter Kennedy,et al.  Nonlinear analysis of the Colpitts oscillator and applications to design , 1999 .

[22]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[23]  A. Tamasevicius,et al.  Experimental demonstration of chaos from Colpitts oscillator in VHF and UHF ranges , 2004 .

[24]  Michael Peter Kennedy,et al.  The Colpitts oscillator: Families of periodic solutions and their bifurcations , 2000, Int. J. Bifurc. Chaos.

[25]  A. Tamaševičius,et al.  Coupled Chaotic Colpitts Oscillators: Identical and Mismatched Cases , 2006 .

[26]  Li Guo-Hui.  Synchronization and anti-synchronization of Colpitts oscillators using active control , 2005 .

[27]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[28]  L. Ran,et al.  Design of Chaotic Colpitts Oscillator with Prescribed Frequency Distribution , 2004 .

[29]  A. Uchida,et al.  Dual synchronization of chaos in Colpitts electronic oscillators and its applications for communications. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  A. Tamasevicius,et al.  Towards microwave chaos with two-stage Colpitts oscillator , 2001 .

[31]  Shawn D. Pethel,et al.  New Method for the Control of Fast Chaotic Oscillations , 1999 .