Shear, Not Coherence, Organizes chaotic response under Higher-Order Coupling
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917394658623488 |
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| author | Luo, Kaiming |
| author_facet | Luo, Kaiming |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_07842 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Shear, Not Coherence, Organizes chaotic response under Higher-Order Coupling Luo, Kaiming Chaotic Dynamics 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. |
| title | Shear, Not Coherence, Organizes chaotic response under Higher-Order Coupling |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2604.07842 |