Vol. 57

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

Effects of Chaotic Perturbation on a Periodic Gunn Oscillator

By Bishnu Charan Sarkar, Suvra Sarkar, Arun Kanti Guin, and Chaitali Koley
Progress In Electromagnetics Research C, Vol. 57, 13-24, 2015


We have studied dynamics of a periodic X-band Gunn oscillator (GO) forced by microwave chaotic signals through numerical simulation and by hardware experiment. The chaos used as forcing signal is generated in a periodically driven non-oscillatory GO. Numerical simulation results indicate that the forced periodic GO becomes chaotic for a moderate strength of forcing chaos. The generated chaos in driven GO is found to become phase or general synchronized to the forcing chaos depending on strength of the latter one. Hardware experiments are performed in X-band of microwave frequency. It shows generation of chaos in driven GO due to forcing. Moreover, synchronization between forcing and generated chaos is indirectly verified.


Bishnu Charan Sarkar, Suvra Sarkar, Arun Kanti Guin, and Chaitali Koley, "Effects of Chaotic Perturbation on a Periodic Gunn Oscillator," Progress In Electromagnetics Research C, Vol. 57, 13-24, 2015.


    1. Adler, R., "A study of locking phenomena in oscillators," Proceedings of the IEEE, Vol. 61, 1380-1385, 1973.

    2. Diakoku, K. and Y. Mizushima, "Properties of injection locking in the non-linear oscillator," International Journal of Electronics, Vol. 31, 279-292, 1971.

    3. Jensen, R. V., "Synchronization of driven nonlinear oscillators," American J. Physics, Vol. 70, 607-619, 2002.

    4. Rajavi, B., "A study of injection locking and pulling in oscillators," IEEE Journal of Solid State Circuits, Vol. 39, 1415-1424, 2004.

    5. Li, C. J., C. H. Hsiao, F. K. Wang, T. S. Horng, and K. C. Peng, "A rigorous analysis of a phase locked oscillator under injection," IEEE Transactions on Microwave Theory and Techniques, Vol. 58, No. 5, 1391-1400, 2010.

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

    7. Stogartz, S. H., Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, Levant Books, Kolkata, India, (Indian Edition), 2007.

    8. Kurokawa, K., "Injection locking of microwave solid state oscillator," Proceedings of the IEEE, Vol. 61, 1386-1410, 1973.

    9. Alekseev, Y. I., "Determination of basic characteristics of synchronization of Gunn self-excited oscillators," Instruments and Experimental Techniques, Vol. 50, 241-243, 2007.

    10. Main, E. and D. Coffing, "FM demodulation using an injection locked oscillator," IEEE MTT-S International Microwave Symposium Digest, Vol. 1, 135-138, 2000.

    11. Ko, D. S., S. J. Lee, T. J. Baek, S. G. Choi, M. Han, H. C. Park, J. K. Rhee, J. H. Jung, and Y. W. Park, "New tuning method for 94GHz waveguide voltage controlled oscillator," IEEE Microwave and Wireless Components Letters,, Vol. 21, 2011.

    12. Bates, R. S. and S. Feeney, "Novel varactor tuned millimeter wave Gunn oscillator," Electronics Letters, Vol. 23, 714-715, 1987.

    13. Zhu, X., Y. Chen, and W. Hong, "Q-band injection-locked Gunn diode oscillator," International Journal of Infrared and Millimeter Waves, Vol. 17, No. 3, 527-533, 1996.

    14. Mosekilde, E., et al., "Mode locking and spatio-temporal chaos in periodically driven Gunn diode," Physical Review B, Vol. 41, 2298-2306, 1990.

    15. Zongfu, J. and M. Benkun, "Period doubling and chaos in the Gunn effect," Physical Review B, Vol. 44, 11072–4, 1991.

    16. Chakraborty, J., T. Banerjee, R. Ghatak, A. Bose, and B. C. Sarkar, "Generating chaos in injection-synchronized Gunn oscillator: An experimental approach," IETE Journal of Research, Vol. 55, 106-111, 2009.

    17. 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.

    18. Siewe, M. S., H. Cao, and M. A. F. Sanjuan, "Effect of nonlinear dissipation on the basin boundaries of a driven two-well rayleigh-duffing oscillator," Chaos, Solitons and Fractals, Vol. 39, 1092-1099, 2009.

    19. Musielak, D. E., Z. E. Musielak, and J. W. Banner, "Chaos and route to chaos in coupled duffing oscillators with multiple degree of freedom," Chaos, Solitons and Fractals, Vol. 24, No. 4, 907-922, 2005.

    20. 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.

    21. Shi, Z. G. and L. X. Ran, "Microwave chaotic Colpitts oscillator: Design, implementation and applications," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1335-1349, 2006.

    22. 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.

    23. Ram, R. J., R. Sporer, H. R. Blank, and R. A. York, "Chaotic dynamics in coupled microwave oscillators," IEEE Transactions on Microwave Theory and Techniques, Vol. 48, 1909-1916, 2000.

    24. Chakravorty, J., S. Sarkar, and B. C. Sarkar, "Studies on the dynamics of driven bilaterally coupled Gunn oscillator," Indian Journal of Science and Technology, Vol. 7, 916-923, 2014.

    25. Volos, C. K., I. M. Kyprianidis, and I. N. Stouboulos, "Experimental synchronization of two resistively coupled Duffing type circuits," Nonlinear Phenomena in Complex Systems, Vol. 11, 187-192, 2008.

    26. Zhigang, Z., X. Wang, and M. C. Cross, "Transition from partial to complete generalized synchronization in bilaterally coupled chaotic oscillators," Physical Review E, Vol. 65, 056211, 2002.

    27. Sarkar, B. C., "Nonlinear dynamics of Gunn oscillator,” (Book chapter)," New Research Trends in Nonlinear Circuits: Design, Chaotic Phenomena and Applications, Chapter 2, Nova Publishers, 2014.

    28. Sarkar, B. C., S. Sarkar, C. Koley, A. K. Guin, and T. Banerjee, "Effects of unilateral coupling between two chaotic X-band Gunn oscillators," International Journal of Bifurcation and Chaos, Vol. 23, 1350185-1-1350185-23, 2013.

    29. Wolf, A., J. B. Swift, H. Swinney, and J. A. Vastano, "Determining Lyapunov exponents from a time series," Physica D, Vol. 16, 285-317, 1985.

    30. Romano, M. C., M. Theil, J. Kurths, Z. I. Kiss, and J. L. Hudson, "Detection of synchronization for non phase coherent and non stationary data," Europhysics Letters, Vol. 71, 462-472, 2005.

    31. Marwan, N., M. Romano, M. Thiel, and J. Kurths, "Recurrence plots for the analysis of complex system," Physics Reports, Vol. 438, 237-329, 2007.

    32. Rulkov, N. F., M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, "Generalized synchronization of chaos in directionally coupled chaotic systems," Physical Review E, Vol. 51, 980-994, 1995.

    33. Abarbanel, H. D. I., N. F. Rulkov, and M. M. Sushchik, "Generalized synchronization of chaos: The auxiliary system approach," Physical Review E, Vol. 53, 4528-4535, 1996.

    34. 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.