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.
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