Evolving Chaos: Identifying New Attractors of the Generalised Lorenz Family

TL;DR

This paper uses genetic programming to automatically discover over 150 new Lorenz-like chaotic attractors with unique dynamics, expanding the known family of chaotic systems for potential real-world applications.

Contribution

The study introduces a novel evolutionary approach to generate a large family of new chaotic attractors with different nonlinearities from the Lorenz system.

Findings

Over 150 new chaotic attractors identified

Each attractor has unique phase space dynamics

Largest Lyapunov Exponents calculated for all systems

Abstract

In a recent paper, we presented an intelligent evolutionary search technique through genetic programming (GP) for finding new analytical expressions of nonlinear dynamical systems, similar to the classical Lorenz attractor's which also exhibit chaotic behaviour in the phase space. In this paper, we extend our previous finding to explore yet another gallery of new chaotic attractors which are derived from the original Lorenz system of equations. Compared to the previous exploration with sinusoidal type transcendental nonlinearity, here we focus on only cross-product and higher-power type nonlinearities in the three state equations. We here report over 150 different structures of chaotic attractors along with their one set of parameter values, phase space dynamics and the Largest Lyapunov Exponents (LLE). The expressions of these new Lorenz-like nonlinear dynamical systems have been automatically evolved through multi-gene genetic programming (MGGP). In the past two decades, there have been many claims of designing new chaotic attractors as an incremental extension of the Lorenz family. We provide here a large family of chaotic systems whose structure closely resemble the original Lorenz system but with drastically different phase space dynamics. This advances the state of the art knowledge of discovering new chaotic systems which can find application in many real-world problems. This work may also find its archival value in future in the domain of new chaotic system discovery.