Periodic oscillators, isochronous centers and resonance

TL;DR

This paper extends the classical resonance theory from harmonic oscillators to nonlinear isochronous oscillators, analyzing how periodic forcing can lead to unbounded solutions and resonance phenomena.

Contribution

It introduces a generalized framework for understanding resonance in nonlinear isochronous oscillators, expanding classical results beyond harmonic systems.

Findings

Resonance can cause unbounded solutions in nonlinear isochronous oscillators.

The theory of resonance is extended from harmonic to nonlinear isochronous systems.

Conditions under which resonance occurs in these systems are characterized.

Abstract

An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context, resonance means that all solutions are unbounded. The theory of resonance is well known for the harmonic oscillator and we extend it to nonlinear isochronous oscillators.