Vol. 28
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2013-01-24
Studies on the Dynamics of Two Bilaterally Coupled Periodic Gunn Oscillators Using Melnikov Techniques
By
Progress In Electromagnetics Research M, Vol. 28, 213-228, 2013
Abstract
Dynamical stability of a system of bilaterally coupled periodic Gunn oscillators (BCPGO) has been studied employing Melnikov's global perturbation technique. In the BCPGO system, a fractional part of the output signal of one oscillator is injected into the other through a coupling network. The injected signal is considered as a perturbation on the free running dynamics of the receiving oscillator and the amount of perturbation is quantified by a parameter named coupling factor (CF). The limiting values of CFs leading to chaotic dynamics of the BCPGO system are predicted analytically by calculating the Melnikov functions (MFs) in the respective cases. Also the effect of the frequency detuning (FD) between the Gunn Oscillators (GOs) on the computed values of MFs has been examined. A thorough numerical simulation of the BCPGO dynamics has been done by solving the system equations. The obtained results are in qualitative agreement with the analytically predicted observations regarding the roles of the system parameters like CF and FD.
Citation
Bishnu Charan Sarkar, Manoj Dandapathak, Suvra Sarkar, and Tanmoy Banerjee, "Studies on the Dynamics of Two Bilaterally Coupled Periodic Gunn Oscillators Using Melnikov Techniques," Progress In Electromagnetics Research M, Vol. 28, 213-228, 2013.
doi:10.2528/PIERM12120316
References

1. Kuramoto, Y., Chemical Oscillations, Waves and Turbulence, Springer, Berlin, 1984.
doi:10.1007/978-3-642-69689-3

2. Boi, S., I. D. Couzin, N. D. Buono, N. R. Franks, and N. F. Britton, "Coupled oscillators and activity waves in ant colonies," Proceedings Royal Society, 371-378, 1998.

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

4. 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

5. Crawford, J. A., Advanced Phase Lock Technique,, Artech House Inc., 2008.

6. Liao, P. and R. A. York, "A new phase-shifterless beam scanning technique using arrays of coupled oscillators," IEEE Trans. Microwave Theory and Technique,, Vol. 41, 1810-1815, 1993.
doi:10.1109/22.247927

7. Hilborn, R. C., Chaos and Nonlinear Dynamics, Oxford University Press, 2000.
doi:10.1093/acprof:oso/9780198507239.001.0001

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

9. Anishchenko, V., S. Astakhov, and T. Vadivasova, "Phase dynamics of two coupled oscillators under external periodic force," Europhysics Letters, Vol. 86, 2009.
doi:10.1209/0295-5075/86/30003

10. Vincent, U. E. and A. Kenfack, "Synchronization and bifurcation structures in coupled periodically forced non-identical duffing oscillators," Physica Scripta, Vol. 77, 1-7, 2008.
doi:10.1088/0031-8949/77/04/045005

11. Cenys, A., A. Tamasevicius, A. Baziliauskus, R. Krivickas, and E. Lindberg, "Hyperchaos in coupled Colpitts oscillators," Chaos, Solitons and Fractals, Vol. 17, 349-353, 2003.
doi:10.1016/S0960-0779(02)00373-9

12. 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.

13. Sarkar, B. C., C. Koley, A. K. Guin, and S. Sarkar, "Studies on the dynamics of a system of bilaterally coupled chaotic Gunn oscillators," Progress In Electromagnetics Research B, Vol. 42, 93-113, 2012.

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

15. Holmes, J. P. and J. E. Marsden, "Melnikovs method and Arnold di®usion for perturbation of integrable Hamiltonian systems," Journal of Math. Physics, Vol. 23, No. 4, 669-675, 1982.
doi:10.1063/1.525415

16. Jordan, D. W. and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, 4th Ed., Oxford University Press, New York, 2007.

17. Chacon, R., "Melnikov method approach to control of Homo-clinic/Heteroclinic chaos by weak harmonic excitations," Phil. Trans. R. Soc. A, Vol. 364, 2335-2351, 2006.
doi:10.1098/rsta.2006.1828

18. Sprott, J. C., Chaos Data Analyser Package, Web Address: sprott.physics.wise.edu/cda.htm.