Vol. 42

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Studies on the Dynamics of a System of Bilaterally Coupled Chaotic Gunn Oscillators

By Bishnu Charan Sarkar, Chaitali Koley, Arun Kanti Guin, and Suvra Sarkar
Progress In Electromagnetics Research B, Vol. 42, 93-113, 2012


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.


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.


    1. Stori, D. W., et al., "Dynamics of two strongly coupled Vander Pol oscillators," International Journal of Nonlinear Dynamics, Vol. 7, 143-152, 1982.

    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.

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

    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.

    5. Glova, A. F., "Phase locking of optically coupled lasers," Quantum Electronics, Vol. 33, 283-306, 2003.

    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.

    7. Elson, R. C., et al., "Synchronous behaviour of two coupled biological neurons," Phys. Rev. Lett., Vol. 81, No. 25, 5692-5695, 1998.

    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.

    9. Kurokawa, K., "Injection locking of microwave solid state oscillator," Proc. IEEE, Vol. 61, 1386-1410, 1973.

    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.

    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.

    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.

    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.

    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 .

    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.

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

    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.

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

    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.

    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.

    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.

    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.

    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.

    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.

    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.

    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.