Feedback-induced self-oscillations in large interacting systems subjected to phase transitions

Authored by Martino Daniele De

Date Published: 2019

DOI: 10.1088/1751-8121/aaf2dd

Sponsors: European Union

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

In this article it is shown that large systems with many interacting units endowing multiple phases display self-oscillations in the presence of linear feedback between the control and order parameters, where an Andronov- Hopf bifurcation takes over the phase transition. This is simply illustrated through the mean field Landau theory whose feedback dynamics turn out to be described by the Van der PoI equation and it is then validated for the fully connected Ising model following heat bath dynamics. Despite its simplicity, this theory accounts potentially for a rich range of phenomena: here it is applied to describe in a stylized way (i) excess demand-price cycles due to strong herding in a simple agent-based market model; (ii) congestion waves in queuing networks triggered by user feedback to delays in overloaded conditions; and (iii) metabolic network oscillations resulting from cell growth control in a bistable phenotypic landscape.

Tags

Agent-based models Dynamics Ising model phase transitions Model queuing networks Statistical-mechanics Metabolic networks Self-oscillations