Nonlinear electronic circuit, Part I: Multiple routes to chaos

Abstract

A nonlinear electronic oscillator, suitable for synchronized chaotic communication, is studied. This circuit is capable of transmitting discrete chaotic signals, although the chaotic modes of operation are controlled in an analog way. In Part I of this review paper the three routes to chaotic operation that appear, namely the period doubling, intermittency and crisis induced intermittency, are thoroughly studied and discussed. In all three routes to chaos the appropriate experimental distributions were calculated. Moreover, the chaotic nature of the circuit operation was evaluated by using the Grassberger–Procaccia method. Calculation of the corresponding minimum embedding dimension, the Kolmogorov–Sinai entropy as well as the maximal Lyapunov exponent give useful information in order to fully characterize the circuit operation.