Nonlinear analysis of a classical double oscillator model

TL;DR

This paper analyzes a classical double oscillator model, exploring its dynamics, bifurcations, and chaos, especially under periodic forcing, revealing complex behaviors including chaos.

Contribution

It provides a qualitative analysis of the double oscillator's dynamics, including bifurcations and chaos, under various parameter limits and forcing conditions.

Findings

Identification of bifurcation points leading to chaos

Chaotic behavior emergence under periodic forcing

Qualitative orbit analysis around equilibrium points

Abstract

A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative analysis of orbits around the equilibrium points, period-doubling bifurcation, time series curves, surfaces of section and Poincare maps. An interesting outcome of our findings is the emergence of chaotic behavior when the system is confronted with a periodic force term like fcos{\omega}t.