Diversity and Temporality of Chaotic Events

Abstract

Publications dealing with chaos usually exhibit an image of a single, truncated and always expanding chaotic event in the system in which chaos is being reported. This generates the impression that chaotic events are unique and once they start, they increase intensity ad infinitum, eventually taking control of the system, and lasting forever. With the aim on finding out whether the above described panorama is correct, an investigation was carried out on the nonlinear damped and forced oscillator (NLDFO). It was encountered a diversity of chaotic events and that those have a beginning and an end, this is, they are temporal. Additionally it has been observed that chaotic events initially generate a series of period bifurcations increasing their intensity and then by collapsing bifurcations this intensity gradually decreases until chaos vanishes. The largest Lyapunov exponents of the displayed chaotic events, as well as some general observations about chaotic events in the NLDFO are reported.