Parametrically driven instability in quasi-reversal systems

Parametric instability of quasi-reversal system i.e. time reversible systems perturbed with injection and dissipation of energy is studied in a unified manner. We infer and characterize an adequate amplitude equation, which is the parametrically driven damped nonlinear Schrödinger equation, corrected with higher order terms. This model exhibits rich dynamical behavior which are lost in the parametrically driven damped nonlinear Schrödinger equation such as: uniform states, fronts and coherent states. The dynamical behavior of a simple parametrically driven system, the vertically driven chain of pendula, exhibits quite good agreement with the amended amplitude equation.