Approximating an Exactly Solvable Chaotic Oscillator Using a Colpitts Oscillator Circuit

Abstract

An alternative approximate implementation of an exactly solvable chaotic oscillator circuit is presented. In this implementation, the previously used op amp based NIC sinusoidal oscillator subcircuit was replaced with a single BJT Colpitts oscillator subcircuit. Although this change resulted in an increase in the order of the chaotic system and introduced additional nonlinearities, simulation and hardware testing results indicated that its performance was equivalent to that of the mathematical model for the exactly solvable chaotic system. It also demonstrated equivalent performance to previous op amp based designs, while mitigating some of the performance limitations inherent with op amp based NICs. Evaluation of the resulting 18.9 kHz oscillator circuit demonstrated chaotic dynamics comparable to those from the ideal exactly solvable chaotic system.