Computation of the Largest Lyapunov Exponent Using SPICE-Like Programs

Abstract

This paper presents a novel method for calculating the positive largest Lyapunov exponent (LLE) using only SPICE-like programs. The LLE is a measure of the rate of divergence of nearby trajectories in phase space and is an important indicator of chaotic behavior. The proposed method calculates the LLE directly from systems represented in schematic circuits, inspired by interval extensions that exploit divergent trajectories to calculate the lower-bound error. The exponent is obtained from the slope of the line derived from the lower-bound error, using a differential amplifier to quantify it, along with a straightforward linear fit to the logarithm of the divergence of two circuits’ trajectories. This approach is unique as it requires only user skills in SPICE-like programs, unlike most other approaches, providing a simple, efficient, and accurate way to analyze and characterize chaotic dynamics. Results demonstrate that the suggested method successfully estimated the LLE for two well-known systems.