Emergence of collective self-oscillations in minimal lattice models with feedback
The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in dynamical systems theory, this phenomenon is not well understood in the context of out-of-equilibrium phase transitions. Here we consider classical lattice models, name...
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Zusammenfassung: | The emergence of collective oscillations and synchronization is a widespread
phenomenon in complex systems. While widely studied in dynamical systems
theory, this phenomenon is not well understood in the context of
out-of-equilibrium phase transitions. Here we consider classical lattice
models, namely the Ising, the Blume-Capel and the Potts models, with a feedback
among the order and control parameters. With linear response theory we derive
low-dimensional dynamical systems for mean field cases that quantitatively
reproduce many-body stochastic simulations. In general, we find that the usual
equilibrium phase transitions are taken over by complex bifurcations where
self-oscillations emerge, a behavior that we illustrate by the feedback Landau
theory. For the case of the Ising model, we obtain that the bifurcation that
takes over the critical point is non-trivial in finite dimensions. We provide
numerical evidence that in 2D the most probable value of the amplitude follows
the Onsager law. We illustrate multi-stability for the case of discontinuously
emerging oscillations in the Blume-Capel model, whose tricritical point is
substituted by the Bautin bifurcation. For the Potts model with q = 3 colors we
highlight the appearance of two mirror stable limit cycles at a bifurcation
line and characterize the onset of chaotic oscillations that emerge at low
temperature through either the Feigenbaum cascade of period doubling or the
Aifraimovich-Shilnikov scenario of a torus destruction. We show that entropy
production singularities as a function of the temperature correspond to change
in the spectrum of Lyapunov exponents. Our results show that mean-field
behaviour can be described by the bifurcation theory of low-dimensional
dynamical systems, which paves the way for the definition of universality
classes of collective oscillations. |
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DOI: | 10.48550/arxiv.2306.01823 |