Heterogeneity-induced chaos in globally coupled Stuart--Landau oscillators

Luekai Zhao; Nariya Uchida

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arXiv · 2610.08239

Heterogeneity-induced chaos in globally coupled Stuart--Landau oscillators

Luekai Zhao·Nariya Uchida

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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 RIS

Luekai Zhao, Nariya Uchida. 2026-10-06. Heterogeneity-induced chaos in globally coupled Stuart--Landau oscillators. https://arxiv.org/abs/2610.08239

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