Attractor selection in nonlinear oscillators by temporary dual-frequency driving

Abstract

This paper presents a control technique capable of driving a harmonically driven nonlinear system between two distinct periodic orbits. A vital component of the method is a temporary dual-frequency driving with tunable driving amplitudes. Theoretical considerations revealed two necessary conditions: one for the frequency ratio of the dual-frequency driving and another one for torsion numbers of the two orbits connected by bifurcation curves in the extended dual-frequency driving parameter space. Although the initial and the final states of the control strategy are single-frequency driven systems with distinct parameter sets (frequencies and driving amplitudes), control of multistability is also possible via additional parameter tuning. The technique is demonstrated on the symmetric Duffing oscillator and the asymmetric Toda oscillator.