Wada property in systems with delay

TL;DR

This paper investigates how delay differential equations can induce chaos and unpredictability, focusing on the Wada property, which causes sensitive dependence on initial conditions in systems with delay.

Contribution

It explores the relationship between delay and the Wada property, revealing how small variations in history functions can drastically alter system outcomes.

Findings

Delay can induce chaos in predictable systems

Wada property causes sensitive dependence on initial conditions

Small changes in history lead to different final states

Abstract

Delay differential equations take into account the transmission time of the information. These delayed signals may turn a predictable system into chaotic, with the usual fractalization of the phase space. In this work, we study the connection between delay and unpredictability, in particular we focus on the Wada property in systems with delay. This topological property gives rise to dramatical changes in the final state for small changes in the history functions.