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

D. De Martino, Journal of Physics A: Mathematical and Theoretical 52 (2019) 045002.

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Journal Article | Published | English
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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.
Publishing Year
Date Published
2019-01-07
Journal Title
Journal of Physics A: Mathematical and Theoretical
Volume
52
Issue
4
Article Number
045002
IST-REx-ID

Cite this

De Martino D. Feedback-induced self-oscillations in large interacting systems subjected to phase transitions. Journal of Physics A: Mathematical and Theoretical. 2019;52(4):045002. doi:10.1088/1751-8121/aaf2dd
De Martino, D. (2019). Feedback-induced self-oscillations in large interacting systems subjected to phase transitions. Journal of Physics A: Mathematical and Theoretical, 52(4), 045002. https://doi.org/10.1088/1751-8121/aaf2dd
De Martino, Daniele. “Feedback-Induced Self-Oscillations in Large Interacting Systems Subjected to Phase Transitions.” Journal of Physics A: Mathematical and Theoretical 52, no. 4 (2019): 045002. https://doi.org/10.1088/1751-8121/aaf2dd.
D. De Martino, “Feedback-induced self-oscillations in large interacting systems subjected to phase transitions,” Journal of Physics A: Mathematical and Theoretical, vol. 52, no. 4, p. 045002, 2019.
De Martino D. 2019. Feedback-induced self-oscillations in large interacting systems subjected to phase transitions. Journal of Physics A: Mathematical and Theoretical. 52(4), 045002.
De Martino, Daniele. “Feedback-Induced Self-Oscillations in Large Interacting Systems Subjected to Phase Transitions.” Journal of Physics A: Mathematical and Theoretical, vol. 52, no. 4, IOP Publishing, 2019, p. 045002, doi:10.1088/1751-8121/aaf2dd.
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