Nonlinearity-induced symmetry breaking in a system of two parametrically driven Kerr-Duffing oscillators

We study the classical dynamics of a system comprising a pair of Kerr-Duffing nonlinear oscillators, which are coupled through a nonlinear interaction and subjected to a parametric drive. Using the rotating wave approximation, we analyze the steady-state solutions for the amplitudes of the two oscillators. For the case of almost identical oscillators, we investigate separately the cases in which only one oscillator is parametrically driven and in which both oscillators are simultaneously driven. In the latter regime, we demonstrate that even when the parametric drives acting on the two oscillators are identical, the system can transition from a stable symmetric solution to a broken-symmetry solution as the detuning is varied.