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

Daniele De Martino

doi:10.1088/1751-8121/aaf2dd

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 Pol 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.

Highlights

From clocks to motors [1], many musical instruments [2, 3], pumping hearts [5], and firing neurons [6], many oscillatory systems are self-sustained [1]
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
While in the Ising model the feedback is artificially introduced for illustrative purposes, several different phenomena are considered in a stylized way in which the feedback is fully dynamically justified, namely (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; (iii) metabolic network oscillations resulting from cell growth control in a bistable phenotypic landscape

Summary

Introduction

From clocks to motors [1], many musical instruments [2, 3] (including our throat [4]), pumping hearts [5], and firing neurons [6], many oscillatory systems are self-sustained [1]. 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.

Results

Conclusion