The Higher the Damping, the Lower the Chaos Intensity (pp. 253-260)
Authors: Javier Montenegro Joo
Abstract: An investigation on how the damping of the environment modifies the chaotic behavior of an oscillator has been carried out. The mathematical model used is that of the nonlinear damped and forced oscillator (NLDFO) and it has been encountered that -as it is intuitively expected- the chaotic behavior is reduced when the damping the oscillator is subject to is increased; this is confirmed by the decreasing values of the corresponding characteristic Lyapunov exponents. Additionally it has also been detected that ľas predictable- the Kolmogorov entropy decreases when damping is increased. Since the NLDFO transitions towards chaos through period bifurcation cascades, in order to visualize and compare the effect of the damping on its chaotic behavior, bifurcation cascades corresponding to different values of the damping are displayed, these show high intensity chaos when the damping is low and, almost no chaos when the damping is rather high.