Coexistence of Subharmonic Resonant Modes Obeying a Period-Adding Rule

Abstract

We report numerical evidence of a novel chain of subharmonic resonances organized in period-adding domains in the parameter space. Different periodic domains are mediated by a coexisting main subharmonic motion according to a hierarchical organization rule. We consider the driven bilinear oscillator — which is the simplest system to model a range of engineering systems going from cracked mechanical structures to switching electronic circuits — and show that its parameter space is marked by multistability involving subharmonic main modes, as well as period-adding secondary modes which, through a period-doubling route, lead to coexisting chaotic attractors.