Non-linear Reasonant Systems: Bifurcation and Chaos Development of a Fast Fourier Transform Driver

Abstract

The response of non-linear resonant systems driven sinusoidally at resonance has complicated dependence on the amplitute of the driving signal. Chaos and bifurcation in driven non-linear resonant systems are examined here in two ways. First, an experimental investigation of a simple electrical circuit (series L-R-diode) exhibiting chaos and bifurcation; second, a Fast Fourier Transform (FFT) analysis of a simple numerical model of such systems as provided by S. Rajnak. FFT analysis was achieved through the implementation on the VAX of the FORTRAN routines of Weinstein, et. al. A "driver shell" was written in FORTRAN, based on an example contained in Weinstein et al, to enable less sophisticated users to obtain FFT's of their data.