Nonsingular parametric oscillators Darboux-related to the classical harmonic oscillator
H.C.Rosu, O.Cornejo-Perez, P. Chen
TL;DR
This paper identifies nonsingular parametric oscillators related to the classical harmonic oscillator using a modified factorization method, revealing new dissipative and gain features, and explores their hyperbolic counterparts with transient underdamped behavior.
Contribution
It introduces a modified factorization method to find nonsingular Darboux-related oscillators with unique dissipative and gain properties.
Findings
Identified nonsingular parametric oscillators with periodic dissipative/gain features
Applied the method to hyperbolic oscillators showing transient underdamped behavior
Revealed new Darboux partners with distinctive dynamical properties
Abstract
Interesting nonsingular parametric oscillators which are Darboux related to the classical harmonic oscillator and have periodic dissipative/gain features are identified through a modified factorization method. The same method is applied to the upside-down (hyperbolic) `oscillator' for which the obtained Darboux partners show transient underdamped features
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