Bifurcation Structure of Double Hysteresis and Isolated Branches in a Parametric Duffing Nanoresonator
Abstract
Direct and parametric driving together generate nonlinear response structures beyond conventional Duffing hysteresis, including multiple switching regions and isolated branches. Understanding how these structures are connected requires identifying the bifurcations that reorganize the response as the parametric excitation is varied. At a phase difference of 45 degrees between the direct and parametric excitations, we experimentally and analytically determine how the steady-state response changes as the parametric excitation is increased. A single resonance peak first splits into two while the response remains single valued. Two successive cusp bifurcations then create two saddle-node pairs and establish a double-hysteretic response. At the parametric-instability threshold, one saddle node of each pair is displaced towards unbounded amplitude and detuning, and an isolated-branch structure emerges above threshold. A parametric representation of the steady state distinguishes amplitude extrema from genuine saddle-node bifurcations and provides analytical conditions for these changes. Measurements on a dielectrically actuated pre-stressed SiN nanostring reproduce the predicted response and associated switching behavior. These results establish the bifurcation pathway connecting the different response structures at this phase configuration, providing a systematic basis for controlling multistability and switching in parametrically driven nonlinear resonators.
Related
- Bifurcation structure of soliton self-injection locking in microresonators
- Hysteresis-Driven Radiative Mpemba Effect in Phase-Change Nanostructures
- Exceptional points and hysteresis in Kerr-Newman quasi-normal modes
- A new Fermi kinetic phase transition model for metals including hysteresis effects
- Energy-Based Anisotropic Hysteresis Modeling for Permanent Magnets
BibTeX
@misc{zhang2026bifurcation,
title = {{Bifurcation Structure of Double Hysteresis and Isolated Branches in a Parametric Duffing Nanoresonator}},
author = {Dingda Zhang and Maria Kallergi and Chanyoung So and Eva M. Weig and Ahmed A. Barakat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17052},
eprint = {2610.17052},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17052},
}
RIS
TY - UNPB
TI - Bifurcation Structure of Double Hysteresis and Isolated Branches in a Parametric Duffing Nanoresonator
AU - Dingda Zhang
AU - Maria Kallergi
AU - Chanyoung So
AU - Eva M. Weig
AU - Ahmed A. Barakat
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17052
UR - https://arxiv.org/abs/2610.17052
AB - Direct and parametric driving together generate nonlinear response structures beyond conventional Duffing hysteresis, including multiple switching regions and isolated branches. Understanding how these structures are connected requires identifying the bifurcations that reorganize the response as the parametric excitation is varied. At a phase difference of 45 degrees between the direct and parametric excitations, we experimentally and analytically determine how the steady-state response changes as the parametric excitation is increased. A single resonance peak first splits into two while the response remains single valued. Two successive cusp bifurcations then create two saddle-node pairs and establish a double-hysteretic response. At the parametric-instability threshold, one saddle node of each pair is displaced towards unbounded amplitude and detuning, and an isolated-branch structure emerges above threshold. A parametric representation of the steady state distinguishes amplitude extrema from genuine saddle-node bifurcations and provides analytical conditions for these changes. Measurements on a dielectrically actuated pre-stressed SiN nanostring reproduce the predicted response and associated switching behavior. These results establish the bifurcation pathway connecting the different response structures at this phase configuration, providing a systematic basis for controlling multistability and switching in parametrically driven nonlinear resonators.
ER -