Stabilizing effect of delay in higher dimensions

TL;DR

This paper demonstrates that introducing delays in higher-dimensional linear systems can stabilize otherwise unstable equilibria, extending previous findings from 2x2 systems to 3x3 systems.

Contribution

It generalizes the stabilization effect of delays from 2x2 to 3x3 linear differential systems, providing new insights into delay-induced stabilization.

Findings

Delay can stabilize unstable equilibria in 3x3 systems

Extension of delay stabilization from 2x2 to 3x3 systems

Theoretical framework for delay effects in higher dimensions

Abstract

We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This generalizes one of the cases for $2 \times 2$ systems studied in 'Delay can stabilize: Love affairs dynamic' by N. Bielczyk et al.