NONLINEAR DYNAMICS OF DAMPED AND DRIVEN VELOCITY-DEPENDENT SYSTEMS

In this paper, the nonlinear dynamics of certain damped and forced ver sions of velocity-dependent potential systems, namely, (i) the motion of a particle on a rotating parabola and (ii) a nonlinear harmonic osc illator, is considered. Various bifurcations such as symmetry breaking , period doubling, intermittency, crises,land anti-monotonicity are re ported. We also investigate the transition from two-frequency quasiper iodicity to chaotic behavior in a model for the quasiperiodically driv en rotating parabola system. As the driving parameter is increased, th e route to chaos takes place in four distinct stages. The first stage is a torus doubling bifurcation. The second stage is a merging of doub led 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 attra ctor.