Bifurcation and chaos in a periodically driven quartic oscillator at relativistic energies

Abstract

The classical dynamics of a damped quartic oscillator driven by a sinusoidal force is investigated, with particular attention to the effects that arise when the motion of the oscillator becomes relativistic. Bifurcation diagrams constructed numerically indicate that, as relativistic effects become strong, chaotic behavior exhibited by the oscillator in the nonrelativistic limit at large force amplitude is replaced by a period-1 regular motion. At relativistic energies, therefore, a transition from chaos to a regular motion occurs as the force amplitude is increased beyond a critical value. The transition is seen to occur abruptly with a slight increase of the force amplitude from below to above the critical value. The sudden destruction of the chaotic attractor is probably triggered by the mechanism of crisis.