Simulation of Chua's Circuit by Means of Interval Analysis

TL;DR

This paper explores the simulation of Chua's circuit using interval analysis, revealing how different rounding modes affect the circuit's dynamics and addressing error propagation issues in numerical simulations.

Contribution

It introduces an interval analysis approach to simulate Chua's circuit, highlighting the impact of rounding modes on the circuit's qualitative behavior.

Findings

Different rounding modes qualitatively change circuit dynamics

Interval analysis provides insights into error propagation

Simulation results differ from standard IEEE 754 methods

Abstract

The Chua's circuit is a paradigm for nonlinear scientific studies. It is usually simulated by means of numerical methods under IEEE 754-2008 standard. Although the error propagation problem is well known, little attention has been given to the relationship between this error and inequalities presented in Chua's circuit model. Taking the average of round mode towards $+\infty$ and $-\infty$, we showed a qualitative change on the dynamics of Chua's circuit.