Phenomena of complex analytic dynamics in the systems of alternately excited coupled non-autonomous oscillators and self-sustained oscillators

摘要

A feasible model is introduced that manifests phenomena intrinsic toiterative complex analytic maps (such as the Mandelbrot set and Julia sets).The system is composed of two coupled alternately excited oscillators (orself-sustained oscillators). The idea is based on a turn-by-turn transfer ofthe excitation from one subsystem to another (S.P.~Kuznetsov, Phys.~Rev.~Lett.\bf 95 \rm, 2005, 144101) accompanied with appropriate nonlinear transformationof the complex amplitude of the oscillations in the course of the process.Analytic and numerical studies are performed. Special attention is paid to ananalysis of the violation of the applicability of the slow amplitude methodwith the decrease in the ratio of the period of the excitation transfer to thebasic period of the oscillations. The main effect is the rotation of theMandelbrot-like set in the complex parameter plane; one more effect is thedestruction of subtle small-scale fractal structure of the set due to thepresence of non-analytic terms in the complex amplitude equations.