Recovering discrete delayed fractional equations from trajectories

TL;DR

This paper demonstrates how machine learning can identify the fractional and delay characteristics of discrete dynamical systems, specifically applied to the fractional delayed logistic map, enabling detection and characterization from observed trajectories.

Contribution

It introduces a method to detect and characterize fractional and delay effects in discrete dynamical systems using machine learning, applied to the fractional delayed logistic map.

Findings

Successfully detects delay effects from trajectories

Accurately characterizes the fractional component

Applicable to the fractional delayed logistic map

Abstract

We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it has some delay effect or not, and also to characterize the fractional component of the underlying generation model.