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.
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
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.