Complex analytic dynamics phenomena in a system of coupled nonautonomous oscillators with alternative excitation

A model system of two coupled nonautonomous oscillators is proposed, in which the phenomena of complex analytic dynamics (Mandelbrot and Julia sets, etc.) characteristic of complex logistic maps are realized. The idea underlying the model is based on the mechanism of alternative excitation transfer from one subsystem to another and on the method (well known in the theory of oscillations) of slowly varying complex amplitudes.