Classical Chaos in a Driven One-Dimensional Quartic Anharmonic Oscillator
Journal
Computation
Journal Volume
12
Journal Issue
12
Start Page
246
ISSN
2079-3197
Date Issued
2024-12-17
Author(s)
Lin, Yun-Hsi
Abstract
In this work, we investigate the transition from regular dynamics to chaotic behavior in a one-dimensional quartic anharmonic classical oscillator driven by a time-dependent external square-wave force. Owing to energy conservation, the motion of an undriven quartic anharmonic oscillator is regular, periodic, and stable. For a driven quartic anharmonic oscillator, the equations of motion cannot be solved analytically due to the presence of an anharmonic term in the potential energy function. Using the fourth-order Runge–Kutta method to numerically solve the equations of motion for the driven quartic anharmonic oscillator, we find that the oscillator motion under the influence of a sufficiently small driving force remains regular, while by gradually increasing the driving force, a series of nonlinear resonances can occur, grow, overlap, and ultimately disappear due to the emergence of chaos.
Subjects
chaos
nonlinear resonances
quartic anharmonic classical oscillators
square-wave forces
SDGs
Publisher
MDPI AG
Type
journal article