arXiv subjects

Nicolas Thomé

Publications and source records attributed to Nicolas Thomé.

4 recordsLinked to original sources

arXiv2026

Amplitude-Defect Mediated Transition to Partial Incoherence -- From Experiment to Theory

Phase-only models have contributed significantly to the understanding of synchronization; however, they do not account for dynamical scenarios where amplitude dynamics matter. This study identifies an amplitude-mediated transition from complete frequency coherence to partial incoherence, observed both in an electrochemical silicon-etching experiment and within a population of globally coupled heterogeneous Stuart-Landau oscillators. Strong coupling introduces a bimodal-amplitude distribution from which the transition to partial incoherence is triggered by successive secondary Hopf bifurcations in low-amplitude oscillators. When these modulations cause oscillators to experience amplitude defects, the winding number changes, converting the secondary frequency into a new, oscillator-specific mean frequency. This mechanism results in a partially incoherent state, in which one amplitude group maintains frequency locking while another develops a dispersed frequency branch. These findings demonstrate that amplitude defects offer a pathway to incoherence that phase-only models cannot capture.

nlin.PS↗

arXiv2026

Origin of Frequency Clusters and Self-Organized Triplet Locking in the Kuramoto Model with Inertia

We investigate the origin of frequency clusters - states where multiple groups of oscillators with distinct mean frequencies coexist. We use the Kuramoto model with inertia, where identical oscillators are globally coupled. First, we study the creation of two frequency clusters in the thermodynamic limit. Via numerical bifurcation analysis, we confirm that two frequency clusters are created by homoclinic bifurcations. Both clusters can lose their phase-synchrony in transcritical or period-doubling bifurcations. Furthermore, we investigate the creation of three frequency clusters in a system of seven oscillators. Here, the frequency clusters are destabilized by a longitudinal and a transversal period-doubling bifurcation, and the frequency clusters are also created by homoclinic bifurcations. We find that the emergence of three or more frequency clusters via a homoclinic bifurcation implies the creation of a triplet locked state, where the frequency differences exhibit a rational relation. Besides the creation of frequency clusters via a homoclinic bifurcation, we state that Hopf bifurcations cannot create frequency clusters in phase oscillators, and frequency clusters can only be created by global bifurcations.

nlin.AO↗

arXiv2025

Synchronized Bimodal Amplitude Patterns in Heterogeneous Oscillatory Media -- Experiment and Theory

We study an intricate mechanism of pattern formation in globally coupled heterogeneous oscillatory media. In anodic electrochemical etching of silicon, the electrode surface splits into two amplitude-phase regions, while all oscillators remain frequency-locked. Additionally, the relative ratio of the pattern can be tuned via a coupling term. We introduce a heterogeneous, complex Ginzburg-Landau equation with global coupling to reproduce these patterns and study their formation. Neglecting diffusion shows that frequency entrainment arises from amplitude adaptation. Diffusion, on the other hand, enforces the selection of a unique cluster ratio. In quantitative agreement with simulations, a center-manifold reduction yields a Lyapunov functional that predicts the selected ratio. Both of these results establish a theoretical framework that connects experiment and theory. Moreover, they show how heterogeneity and diffusion convert degenerate cluster dynamics into robust pattern selection.

nlin.PS↗

arXiv2025

Hierarchical Clustering in Mean-Field Coupled Stuart-Landau Oscillators

Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and incoherent states. Despite their fundamental role in coupled oscillator dynamics, our understanding of how these clusters form and differentiate is still quite limited. Here, we study an ensemble of globally coupled Stuart-Landau oscillators and focus on the question of how 3-cluster solutions emerge from 2-cluster solutions and how the different 3-cluster solutions are organized in parameter space. We show that the arrangement of the clusters is dictated by a co-dimension 2 point, which we coin Type-II cluster singularity. Furthermore, our study points to a hierarchical structure of higher cluster solutions.

nlin.PS↗