Exceptional points in coupled dissipative dynamical systems

TL;DR

This paper investigates the transient dynamics of coupled dissipative systems, revealing that exceptional points characterized by eigenvalue and eigenvector coalescence minimize transient time and relate to critical phenomena like frequency locking.

Contribution

It identifies and analyzes exceptional points in coupled dissipative systems, linking them to transient behavior and critical transitions such as amplitude death and frequency locking.

Findings

Transient time is minimized at exceptional points.

Eigenvalues and eigenvectors coalesce at these points.

Exceptional points are linked to critical frequency locking.

Abstract

We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of Jacobian matrix coalesce at the same time, this degenerate point is called the exceptional point. For the case of coupled limit cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.