Shear, Not Coherence, Organizes chaotic response under Higher-Order Coupling

TL;DR

This study reveals that in chaotic oscillator networks, higher-order interactions influence chaos indirectly by modulating amplitude shear, not through phase coherence.

Contribution

It demonstrates that chaos in higher-order coupled oscillators is governed by effective-frequency shear, shifting focus from coherence to amplitude heterogeneity.

Findings

Higher-order coupling reconstructs existing chaos rather than creating new chaos.

Chaos is organized by amplitude shear, not phase coherence.

Lyapunov exponents collapse onto a shear-based description.

Abstract

What dynamical quantity is actually controlled by higher-order interactions in chaotic oscillator networks remains unclear. In amplitude-active systems, chaos is often interpreted through coherence, yet coherence is not the quantity that governs instability. In this work, we study a minimal globally coupled quartet of nonisochronous Stuart-Landau oscillators with pairwise and symmetric three-body interactions. The pairwise baseline already supports a connected chaotic branch, and higher-order coupling reconstructs rather than creates this irregular dynamics. We show that chaos is organized not by phase coherence but by effective-frequency shear: higher-order coupling regulates amplitude heterogeneity, which nonisochronicity converts into shear, and shear controls how chaos is expressed under higher-order coupling. The Lyapunov response collapses onto a reduced shear-based description, revealing an indirect control pathway. These results establish that higher-order interactions control chaos only indirectly, by regulating an amplitude-shear mechanism rather than acting directly on synchrony.