Asymptotic convergence for the dynamics of a Duffing-like oscillator under scaling analyses

André Luís Prando Livorati; André Paganotti Faber; Daniel Borin

doi:10.1063/5.0233700

Asymptotic convergence for the dynamics of a Duffing-like oscillator under scaling analyses

Chaos. 2025 Jan 1;35(1):013108. doi: 10.1063/5.0233700.

Authors

André Luís Prando Livorati¹, André Paganotti Faber¹, Daniel Borin¹

Affiliation

¹ IGCE-Physics Department, São Paulo State University (UNESP), 13506-900 Rio Claro, SP, Brazil.

PMID: 39752193
DOI: 10.1063/5.0233700

Abstract

The dynamics of the convergence for the stationary state considering a Duffing-like equation are investigated. The driven potential for these dynamics is supplied by a damped forced oscillator that has a piecewise linear function. Fixed points and their basins of attraction were identified and measured. We used entropy basin techniques to characterize the basins of attraction, where a changeover in its boundary basin entropy is observed concerning the boundary length. Additionally, we have a set of polar coordinates to describe the asymptotic convergence of the dynamics based on the range of the control parameter and initial conditions. The entire convergence to the stationary state was characterized by scaling laws.