Ghost channels and ghost cycles guiding long transients in dynamical systems

TL;DR

This paper introduces ghost channels and ghost cycles as a new framework to explain long transient dynamics in natural systems, especially when traditional saddle-based models are insufficient due to noise and uncertainty.

Contribution

It generalizes the concept of ghost states to include ghost channels and cycles, providing a robust framework for modeling long transients without relying on fixed points.

Findings

Ghost channels and cycles organize slow directed flows in dynamical systems.

These objects emerge broadly in models of natural systems.

The framework explains robust long transients beyond saddle-based dynamics.

Abstract

Dynamical descriptions and modeling of natural systems have generally focused on fixed points, with saddles and saddle-based phase-space objects such as heteroclinic channels/cycles being central concepts behind the emergence of quasi-stable long transients. Reliable and robust transient dynamics observed for real, inherently noisy systems is, however, not met by saddle-based dynamics, as demonstrated here. Generalizing the notion of ghost states, we provide a complementary framework that does not rely on the precise knowledge or existence of (un)stable fixed points, but rather on slow directed flows organized by ghost sets in ghost channels and ghost cycles. Moreover, we show that appearance of these novel objects is an emergent property of a broad class of models, typically used for description of natural systems.