https://doi.org/10.1140/epjs/s11734-025-02035-7
Regular Article
Active matter synchronization and synergetics
1
ETH Zurich, Weinbergstrasse 58, 8092, Zurich, Switzerland
2
Faculty of Behavioural and Social Sciences, Sociology/ICS, University of Groningen, Groningen, The Netherlands
a
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Received:
10
June
2025
Accepted:
17
October
2025
Published online:
29
October
2025
Abstract
We study the collective behavior in a stochastic agent-based model of active matter. Provided a critical take-up of energy, agents produce two types of goods x, y that follow a generalized Lotka–Volterra dynamics. For isolated agents, production would either reach a fixed point or diverge. Coupling agents’ production via a mean field of x, however, can lead to synchronized oscillations if agents cooperate in the production of x. The production of y supports the emergence of the synchronized dynamics by suppressing fluctuations and mitigating competition between agents, this way stabilizing the production of x. We find that in the synchronized state different groups of agents coexist, each following their own limit cycle. The Kuramoto order parameter is large within groups, and small across groups. The collective state is stable against shocks from agents temporarily switching between cooperation and competition. The model dynamics illustrates the principles of synergetics, i.e., the spontaneous emergence of order given a critical energy supply and cooperative interactions.
Dedicated to the memory of Hermann Haken.
Present address: Faculty of Behavioural and Social Sciences, Sociology/ICS, University of Groningen, Groningen, The Netherlands
© The Author(s) 2025
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