  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.
