Viscosity Levels and Strength of Chaos

It is intuitively expected that the vibrations of an oscillator be hindered when the viscosity of the medium is increased. The higher the viscosity, the higher the hindering effect. This paper reports the detailed way the viscosity of the environment affects the chaotic vibrations of the nonlinear damped and forced oscillator (NLDFO), which transitions towards chaos through a cascade of period bifurcations. It has been found that when the damping of the environment is increased, the mentioned bifurcation cascades become weaker, implying lower chaos intensity, which is corroborated by the corresponding decreasing values of the Lyapunov exponents and by the descent of the Kolmogorov entropy. It is also informed that the value of the extreme displacement as well as that of extreme velocity during a chaotic event decrease when the damping is increased, which is interpreted as a contraction of the orbit in state space, additionally the effect of the damping on the Return Maps of extreme displacements is described. Furthermore this paper gives account of evidence of serial chaos, which is obtained by extending during a very long time the computer simulation after a chaotic event.