Heterogeneity-induced chaos in globally coupled Stuart--Landau oscillators
Abstract
We show that linear-growth-rate heterogeneity combined with complex global coupling can generate quasiperiodicity and chaos in a finite population of Stuart-Landau oscillators with identical natural frequencies and no Kerr-type nonlinear frequency shift. Lyapunov spectra identify limit cycles, quasiperiodic tori, and chaotic attractors, while the order-parameter amplitude exhibits signatures consistent with period-doubling-like transitions towards chaos. We further derive a finite-size invariant manifold of vanishing-order-parameter phase-locked solutions represented by closed polygons with fixed side lengths and demonstrate their configuration-dependent transverse stability. Ensemble sampling reveals pronounced coexistence among polygonal and ordinary phase-locked cycles, quasiperiodic tori, and chaotic attractors. An amplitude-time rescaling identifies the leading parameter approximately organizing the regime boundaries and the similar bifurcation and multistability patterns. These results advance our understanding of collective dynamics in amplitude-inclusive oscillator networks by revealing how heterogeneity and complex coupling jointly shape dynamical complexity, bifurcation structure, and multistability.
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BibTeX
@misc{zhao2026heterogeneityinduced,
title = {{Heterogeneity-induced chaos in globally coupled Stuart--Landau oscillators}},
author = {Luekai Zhao and Nariya Uchida},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08239},
eprint = {2610.08239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08239},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Heterogeneity-induced chaos in globally coupled Stuart--Landau oscillators
AU - Luekai Zhao
AU - Nariya Uchida
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08239
UR - https://arxiv.org/abs/2610.08239
AB - We show that linear-growth-rate heterogeneity combined with complex global coupling can generate quasiperiodicity and chaos in a finite population of Stuart-Landau oscillators with identical natural frequencies and no Kerr-type nonlinear frequency shift. Lyapunov spectra identify limit cycles, quasiperiodic tori, and chaotic attractors, while the order-parameter amplitude exhibits signatures consistent with period-doubling-like transitions towards chaos. We further derive a finite-size invariant manifold of vanishing-order-parameter phase-locked solutions represented by closed polygons with fixed side lengths and demonstrate their configuration-dependent transverse stability. Ensemble sampling reveals pronounced coexistence among polygonal and ordinary phase-locked cycles, quasiperiodic tori, and chaotic attractors. An amplitude-time rescaling identifies the leading parameter approximately organizing the regime boundaries and the similar bifurcation and multistability patterns. These results advance our understanding of collective dynamics in amplitude-inclusive oscillator networks by revealing how heterogeneity and complex coupling jointly shape dynamical complexity, bifurcation structure, and multistability.
ER -