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PreprintarXiv licencearXiv

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 $|G(3Ω)/G(Ω)|$ is included.

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Cite

BibTeXRIS
BibTeX
@misc{sarkar2026linear,
  title = {{Linear Response Predicts Cusp-Pair Births in Networks with a Localized Cubic}},
  author = {Kanchan Sarkar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11574},
  eprint = {2609.11574},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11574},
}
RIS
TY  - UNPB
TI  - Linear Response Predicts Cusp-Pair Births in Networks with a Localized Cubic
AU  - Kanchan Sarkar
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11574
UR  - https://arxiv.org/abs/2609.11574
AB  - 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 $|G(3Ω)/G(Ω)|$ is included.
ER  -