Dynamics of Non-Autonomous Oscillator with a Controlled Phase and Frequency of External Forcing

TL;DR

This paper investigates how controlling the phase and frequency of external forcing in a non-autonomous oscillator induces complex chaotic and periodic behaviors, revealing a rich structure of oscillatory modes and parameter spaces.

Contribution

It introduces a novel analysis of non-autonomous oscillators with variable external force parameters, highlighting the emergence of complex dynamics and differences from traditional models.

Findings

Chaotic dynamics emerge from controlled phase and frequency variations.

Hierarchy of periodic and chaotic oscillations observed.

Distinct oscillatory modes compared to potential-based non-autonomous oscillators.

Abstract

The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of complex chaotic dynamics in the behavior of oscillator. A hierarchy of various periodic and chaotic oscillations is observed. The paper studies the structure of the space of control parameters. It is shown that in the dynamics of the system there are oscillatory modes similar to those of a non-autonomous oscillator with a potential in the form of a periodic function, but there are also significant differences.