Oscillators with Parametrically Excited Nonlinearity: Resonance, Anti-resonance and Switch

TL;DR

This paper uncovers a new resonance type and anti-resonance in a parametrically excited Van der Pol oscillator, explaining their behaviors and demonstrating how coupled oscillators can function as a sharp amplitude switch.

Contribution

It introduces a novel resonance phenomenon and anti-resonance in a Van der Pol oscillator, along with a method to analyze limiting states under arbitrary periodic excitation and a coupled oscillator switch mechanism.

Findings

Discovery of a new resonance in the Van der Pol oscillator.

Identification of anti-resonance behavior.

Coupled oscillators can act as a sharp amplitude switch.

Abstract

We discover presence of a hitherto unexplored type of resonance in a parametrically excited Van der Pol oscillator. The oscillator also possesses a state of anti-resonance. In the weak non-linear limit, we explain how to practically get a complete picture of different states of limiting oscillations present in the oscillator when the non-linear term therein is excited by an arbitrary $2\pi$ periodic function of time. We also illustrate how two such oscillators can be coupled to behave like a two-state switch allowing an sharp change of value of amplitude for stable oscillations from one constant to another.