Identification of delays and discontinuity points of unknown systems by using synchronization of chaos

TL;DR

This paper introduces a chaos synchronization-based method for identifying delays and discontinuity points in unknown systems, applicable to a wide range of natural and engineered systems.

Contribution

It presents a novel, flexible approach leveraging chaos synchronization to identify delays and discontinuities in diverse dynamical systems.

Findings

Successfully identifies discontinuity points in piecewise systems

Accurately detects delays in delay differential equations

Applicable to various natural and manmade systems

Abstract

In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations and (ii) the delays of systems described by delay differential equations. Delays and discontinuities are widespread features of the dynamics of both natural and manmade systems. The foremost goal of the paper is to present a general and flexible methodology that can be used in a broad variety of identification problems.