Designing Attractive Models via Automated Identification of Chaotic and Oscillatory Dynamical Regimes

TL;DR

This paper introduces a qualitative inference framework that enables the design and reverse engineering of systems with specific chaotic and oscillatory behaviors by directly specifying the desired dynamical attractor features.

Contribution

It presents a novel approach shifting from quantitative data fitting to qualitative dynamics specification for modeling chaotic and oscillatory systems.

Findings

Framework allows direct design of dynamical behaviors

Provides new insights into properties of dynamical systems

Enables reverse engineering of systems with targeted behaviors

Abstract

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an indirect, quantitative approach, e.g. by fitting models to a finite number of data-points. Here we develop a qualitative inference framework that allows us to both reverse engineer and design systems exhibiting these and other dynamical behaviours by directly specifying the desired characteristics of the underlying dynamical attractor. This change in perspective from quantitative to qualitative dynamics, provides fundamental and new insights into the properties of dynamical systems.