Linear Response Predicts Cusp-Pair Births in Networks with a Localized Cubic

Kanchan Sarkar

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arXiv · 2609.11574

Linear Response Predicts Cusp-Pair Births in Networks with a Localized Cubic

Kanchan Sarkar

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Abstract

Linear response is cheap to measure; the bistability boundaries it organizes are not. For a passive network with one localized cubic, the driving-point receptance $G$ fixes the period-one cusp set at fundamental-harmonic order: cusps lie on a fixed phase contour of $G$, a tangency of that contour under parameter variation creates a pair, and its curvature separates a gap opening from an isolated loop. For a two-mode absorber the linear prediction locates a benchmark birth coupling to $0.3\%$, and to $0.03\%$ once a third-harmonic correction of scale $|G(3\Omega)/G(\Omega)|$ is included.

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Kanchan Sarkar. 2026-09-10. Linear Response Predicts Cusp-Pair Births in Networks with a Localized Cubic. https://arxiv.org/abs/2609.11574

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