Chaos suppression of Lorenz Systems by means on the average of rounding modes

TL;DR

This paper introduces a chaos suppression technique for Lorenz systems by averaging rounding modes to reduce errors, transforming chaotic behavior into periodic limit cycles, demonstrated through numerical experiments with Runge-Kutta schemes.

Contribution

It proposes a novel chaos control method using averaging of rounding modes to suppress chaos in Lorenz systems, enhancing stability and predictability.

Findings

Chaos is suppressed to a limit cycle with negative Lyapunov exponent.

Method effectively reduces chaos in Lorenz systems.

Validated across multiple Runge-Kutta discretization schemes.

Abstract

This work deals with chaos suppression based on average of the rounded modes to negative and positive infinite. The present procedure acts to reduce the rounding errors. It was observed that when the method proposed in this paper is applied to the chaotic Lorenz's system, it exhibits a periodic behaviour, characterized by a limit cycle and negative largest Lyapunov exponent. We tested our approach using three discretization schemes based on Runge-Kutta method