English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The emergence of collective oscillations and synchronization is a widespreadphenomenon in complex systems. While widely studied in dynamical systemstheory, this phenomenon is not well understood in the context ofout-of-equilibrium phase transitions. Here we consider classical latticemodels, namely the Ising, the Blume-Capel and the Potts models, with a feedbackamong the order and control parameters. With linear response theory we derivelow-dimensional dynamical systems for mean field cases that quantitativelyreproduce many-body stochastic simulations. In general, we find that the usualequilibrium phase transitions are taken over by complex bifurcations whereself-oscillations emerge, a behavior that we illustrate by the feedback Landautheory. For the case of the Ising model, we obtain that the bifurcation thattakes over the critical point is non-trivial in finite dimensions. We providenumerical evidence that in 2D the most probable value of the amplitude followsthe Onsager law. We illustrate multi-stability for the case of discontinuouslyemerging oscillations in the Blume-Capel model, whose tricritical point issubstituted by the Bautin bifurcation. For the Potts model with q = 3 colors wehighlight the appearance of two mirror stable limit cycles at a bifurcationline and characterize the onset of chaotic oscillations that emerge at lowtemperature through either the Feigenbaum cascade of period doubling or theAifraimovich-Shilnikov scenario of a torus destruction. We show that entropyproduction singularities as a function of the temperature correspond to changein the spectrum of Lyapunov exponents. Our results show that mean-fieldbehaviour can be described by the bifurcation theory of low-dimensionaldynamical systems, which paves the way for the definition of universalityclasses of collective oscillations.

Emergence of collective self-oscillations in minimal lattice models with feedback