Nonlinear dynamics of damped and driven velocity-dependent systems

Abstract

In this paper, the nonlinear dynamics of certain damped and forced versions of velocity-dependent potential systems, namely, (i) the motion of a particle on a rotating parabola and (ii) a nonlinear harmonic oscillator, is considered. Various bifurcations such as symmetry breaking, period doubling, intermittency, crises, and antimonotonicity are reported. We also investigate the transition from two-frequency quasiperiodicity to chaotic behavior in a model for the quasiperiodically driven rotating parabola system. As the driving parameter is increased, the route to chaos takes place in four distinct stages. The first stage is a torus doubling bifurcation. The second stage is a merging of doubled torus. The third stage is a transition from the merged torus to a strange nonchaotic attractor. The final stage is a transition from the strange nonchaotic attractor to a geometrically similar chaotic attractor.