When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming

TL;DR

This paper introduces a novel method using multi-gene genetic programming to automatically generate new chaotic attractors based on the Lorenz system, expanding the diversity of known chaotic structures.

Contribution

The paper presents the first application of MGGP to evolve numerous new chaotic attractors from the Lorenz system, maximizing their Lyapunov exponents.

Findings

Over one hundred new chaotic attractors discovered.

Evolved attractors exhibit higher Lyapunov exponents than original Lorenz system.

Method demonstrates automated exploration of chaotic systems' functional space.

Abstract

In this paper, we propose a novel methodology for automatically finding new chaotic attractors through a computational intelligence technique known as multi-gene genetic programming (MGGP). We apply this technique to the case of the Lorenz attractor and evolve several new chaotic attractors based on the basic Lorenz template. The MGGP algorithm automatically finds new nonlinear expressions for the different state variables starting from the original Lorenz system. The Lyapunov exponents of each of the attractors are calculated numerically based on the time series of the state variables using time delay embedding techniques. The MGGP algorithm tries to search the functional space of the attractors by aiming to maximise the largest Lyapunov exponent (LLE) of the evolved attractors. To demonstrate the potential of the proposed methodology, we report over one hundred new chaotic attractor structures along with their parameters, which are evolved from just the Lorenz system alone.