Computational Complex Dynamics Of The Discrete Lorenz System

TL;DR

This paper explores the discrete dynamics of the Lorenz system with complex variables, a topic not previously studied, and compares it to classical Lorenz systems with real and complex variables.

Contribution

It introduces the first analysis of the discrete Lorenz system with complex variables and compares its dynamics to existing classical models.

Findings

Identifies unique behaviors in the complex discrete Lorenz system

Highlights differences from classical real-variable Lorenz system

Provides insights into complex dynamical phenomena

Abstract

The dynamics of the classical Lorenz system is well studied in $1963$ by E. N. Lorenz. Later on, there have been an extensive studies on the classical Lorenz system with the complex variables and the discrete time Lorenz system with real variables. To the best of knowledge of the author, so far there is no study on discrete time Lorenz system in complex variables. In this article, an attempt has been made to observe and understand the discrete dynamics of the Lorenz system with complex variables. This study compares the discrete dynamics of the Lorenz system with complex variables to that of the classical Lorenz system involving real and complex variables.