Analytic reconstruction of some dynamical systems

TL;DR

This paper presents a method to reconstruct the original dynamical system from a single observed variable, focusing on chaotic systems like Rossler, by deriving candidate models analytically and selecting the most appropriate one.

Contribution

It introduces an analytic approach to reconstructing initial differential equations from limited observational data, applicable to chaotic systems.

Findings

Successfully reconstructs Rossler system from a single variable

Provides a systematic method for model candidate generation

Demonstrates applicability to chaotic dynamical systems

Abstract

We propose a reconstruction of the initial system of ordinary differential equations from a single observed variable. The suggested approach is applied to a certain class of systems which includes, in particular, the Rossler system and other chaotic systems. We develop relations and a method to pass from a model that involves the observable and its time derivatives to a real original system. To this end, we first find a set of candidates of the system in an analytic way. After that, by additionally studying the system, we make a choice for the sought system.