Dynamics of a Charged Thomas Oscillator in an External Magnetic Field

TL;DR

This paper numerically investigates the complex dynamics of a charged Thomas oscillator in an external magnetic field, revealing transitions between chaos, quasi-periodic attractors, and stable limit cycles depending on field strength and damping.

Contribution

It introduces a modified Thomas oscillator model to analyze the effects of magnetic fields on charged particle dynamics, highlighting new behaviors in conservative and dissipative regimes.

Findings

High field strengths lead to quasi-periodic attractors with topology dependent on initial conditions.

Transition from adiabatic motion to chaos as the magnetic field strength decreases.

Chaotic behavior mimics Brownian motion at weak damping and field strength.

Abstract

In this letter, we provide a detailed numerical examination of the dynamics of a charged Thomas oscillator in an external magnetic field. We do so by adopting and then modifying the cyclically symmetric Thomas oscillator to study the dynamics of a charged particle in an external magnetic field. These dynamical behaviours for weak and strong field strength parameters fall under two categories; conservative and dissipative. The system shows a complex quasi-periodic attractor whose topology depends on initial conditions for high field strengths in the conservative regime. There is a transition from adiabatic motion to chaos on decreasing the field strength parameter. In the dissipative regime, the system is chaotic for weak field strength and weak damping but shows a limit cycle for high field strengths. Such behaviour is due to an additional negative feedback loop that comes into action at high field strengths and forces the system dynamics to be stable in periodic oscillations. For weak damping and weak field strength, the system dynamics mimic Brownian motion via chaotic walks.