2012-07-02
Studies on the Dynamics of a System of Bilaterally Coupled Chaotic Gunn Oscillators
By
Progress In Electromagnetics Research B, Vol. 42, 93-113, 2012
Abstract
The dynamics of a system of two bilaterally coupled chaotically oscillating X-band Gunn oscillators (GOs) has been studied by numerical simulation and by hardware experiment. The effect of variation of the coupling strengths between two oscillators in two paths has been explored. The chaotic oscillations in two GOs have become synchronized in most of the cases when coupling factors (CFs) are around 20% or more. However, the transformation of chaotic states of the GOs to quasi-periodic ones has been observed for some values of CFs. A detailed numerical analysis on the instantaneous error parameters of the GO state variables is presented to identify different steady state dynamical conditions of the system. Experimental observations of the GO output frequency power spectra and the averaged product of the two GO outputs in the coupled mode confirm the occurrence of synchronization as well as quenching of chaotic oscillations for different values of CFs.
Citation
Bishnu Charan Sarkar, Chaitali Koley, Arun Kanti Guin, and Suvra Sarkar, "Studies on the Dynamics of a System of Bilaterally Coupled Chaotic Gunn Oscillators," Progress In Electromagnetics Research B, Vol. 42, 93-113, 2012.
doi:10.2528/PIERB12052506
References

1. Stori, D. W., et al. "Dynamics of two strongly coupled Vander Pol oscillators," International Journal of Nonlinear Dynamics, Vol. 7, 143-152, 1982.
doi:10.1016/0020-7462(82)90014-2        Google Scholar

2. Lynch, J. and R. York, "Stability of mode locked states of coupled oscillator array," IEEE Trans. on Circuits and Systems: Fundamental Theory and Applications, Vol. 42, No. 8, 1995.        Google Scholar

3. Anishchenko, V., S. Astakhov, and T. Vadivasova, "Phase dynamics of two coupled oscillators under external periodic force," Europhysics Letters, Vol. 86, 2009.        Google Scholar

4. Ryu, J. and S. Nam, "Very low power single-ended cross-coupled oscillator in CMOS technology," PIERS Proceedings, 1248-1250, Beijing, China, Mar. 26-30, 2007.        Google Scholar

5. Glova, A. F., "Phase locking of optically coupled lasers," Quantum Electronics, Vol. 33, 283-306, 2003.
doi:10.1070/QE2003v033n04ABEH002415        Google Scholar

6. Bhat, G. S., R. Narasimha, and S. Wiggins, "A simple dynamical system that mimics open-flow turbulence," Physics of Fluids A, Vol. 2, 1990.        Google Scholar

7. Elson, R. C., et al. "Synchronous behaviour of two coupled biological neurons," Phys. Rev. Lett., Vol. 81, No. 25, 5692-5695, 1998.
doi:10.1103/PhysRevLett.81.5692        Google Scholar

8. Anishchenko, V. S., A. G. Balanov, N. B. Janson, N. B. Igosheva, and G. V. Bordyugov, "Entrainment between heart rate and weak nonlinear forcing," International Journal of Bifurcation and Chaos, Vol. 10, No. 10, 2339-2348, 2000.
doi:10.1142/S0218127400001468        Google Scholar

9. Kurokawa, K., "Injection locking of microwave solid state oscillator," Proc. IEEE, Vol. 61, 1386-1410, 1973.
doi:10.1109/PROC.1973.9293        Google Scholar

10. Hilborn, R. C., Chaos and Nonlinear Dynamics, Oxford University Press, 2000.

11. Crawford, J. A., Advance Phase Lock Technique, Artech House, Inc., 2008.

12. York, R. A., P. Liao, and J. L. Lynch, "Oscillator array dynamics with broad band N-port coupling networks," IEEE Trans. Microwave Theory and Technique, Vol. 42, No. 11, 1994.
doi:10.1109/22.330116        Google Scholar

13. Ram, R. J., R. Sporer, H. R. Blank, and R. A. York, "Chaotic dynamics in coupled microwave oscillators," IEEE Trans. Microwave Theory and Technique, Vol. 48, 1909-1916, 2000.
doi:10.1109/22.883871        Google Scholar

14. Sarkar, B. C., D. Sarkar, S. Sarkar, and J. Chakraborty, "Studies on the dynamics of bilaterally coupled X-band Gunn oscillators," Progress In Electromagnetics Research B, Vol. 32, 149-167, 2011.
doi:10.2528/PIERB11052201        Google Scholar

15. Jiang, T., S. Qiao, Z.-G. Shi, L. Peng, J. Huangfu, W.-Z. Cui, W. Ma, and L.-X. Ran, "Simulation and experimental evaluation of the radar signal performance of chaotic signals generated from a microwave colpitts oscillator ," Progress In Electromagnetics Research, Vol. 90, 15-30, 2009.
doi:10.2528/PIER08120104        Google Scholar

16. Dmitriev, A. S., A. V. Kletsov, and L. V. Kuzmin, "Experimental generation of chaotic oscillations in microwave band by phase-locked loop," PIERS Proceedings, 1498-1502, Moscow, Russia, Aug. 18-21, 2009 .        Google Scholar

17. Stefanidis, V., O. Tsakiridis, E. Zervas, and J. Stonham, "Design of a microwave chaotic oscillator using symmetric active load," Latest Trends on Circuit, 2010.        Google Scholar

18. Nikishov, A. Y., "Generation of the microwave chaotic oscillations by CMOS structure," PIERS Proceedings, 457-461, Moscow, Russia, Aug. 18-21, 2009.        Google Scholar

19. Pecora, L. M. and T. L. Carroll, Synchronization in chaotic system, Vol. 64, No. 8, 821-825, Phys. Rev. Lett., 1990.

20. Sarkar, B. C., C. Koley, A. K. Guin, and S. Sarkar, "Some numerical and experimental observations on the growth of oscillations in an X-band Gunn oscillator," Progress In Electromagnetics Research B, Vol. 40, 325-341, 2012.        Google Scholar

21. Sprott, J. C., "Chaos data analyzer package,", Web address: sprott.physics.wise.edu/cda.htm .        Google Scholar

22. Osipov, G. V., A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, "Phase synchronization effects in a lattice of nonidentical Rossler oscillators," Phys. Rev. E, Vol. 55, No. 3, 2353-2361, 1997.
doi:10.1103/PhysRevE.55.2353        Google Scholar

23. Krishna, B. M., M. P. John, and V. M. Nandakumaran, "Bidirectional communication using delay coupled chaotic directly modulated semiconductor lasers," Pramana Journal of Physics, Vol. 74, No. 2, 177-188, 2010.
doi:10.1007/s12043-010-0019-6        Google Scholar

24. Zheng, Z., X. Wang, and M. C. Cross, "Transitions from partial to complete generalized synchronizations in bilaterally coupled chaotic oscillators," Phys. Rev. E, Vol. 65, 056211, 2002.
doi:10.1103/PhysRevE.65.056211        Google Scholar

25. Mulet, J., C. Mirasso, T. Heil, and I. Fischer, "Synchronization scenario of two distant mutually coupled semiconductor lasers," Journal of Optics B, Vol. 6, 97-105, 2004.
doi:10.1088/1464-4266/6/1/016        Google Scholar

26. Pikovsky, A., M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, 2003.

27. Vincent, U. E., et al. "Synchronization and basin bifurcations in mutually coupled oscillators," Pramana Journal of Physics, Vol. 68, No. 5, 749-756, 2007.
doi:10.1007/s12043-007-0074-9        Google Scholar

28. Ivanchenko, M. V., G. V. Osipov, V. D. Shalfeev, and J. Kurths, "Synchronization of two non scalar coupled limit cycle oscillators," Physica D, Vol. 189, 8-30, 2004.
doi:10.1016/j.physd.2003.09.035        Google Scholar

29. Sarkar, S., T. Banerjee, D. Mondal, and B. C. Sarkar, "Theory and performance of an electrically controlled microwave phase shifter," Indian Journal of Pure and Applied Physics, Vol. 43, 215-220, 2005.        Google Scholar

30. Sarkar, B. C., D. Ghosh, C. Koley, A. Guin, and S. Sarkar, "Dynamics of a system of bilaterally coupled chaotic Gunn oscillators," PIER Proceedings, 1398-1400, Kuala Lumpur, Malaysia, Mar. 27-30, 2012.        Google Scholar