We introduce a procedure to reveal invariant stable and unstable manifolds, given only experimental data. We assume a model is not available and show how coordinate delay embedding coupled with invariant phase space regions can be used to construct stable and unstable manifolds of an embedded saddle. We show that the method is able to capture the fine structure of the manifold, is independent of dimension, and is efficient relative to previous techniques.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.67.037201 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Soliton and rogue wave excitations in the Chen-Lee-Liu derivative nonlinear Schrödinger equation with two complex PT-symmetric potentials.
Chaos
January 2025
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China.
We demonstrate that fundamental nonlinear localized modes can exist in the Chen-Lee-Liu equation modified by several parity-time (PT) symmetric complex potentials. The explicit formula of analytical solitons is derived from the physically interesting Scarf-II potential, and families of spatial solitons in internal modes are numerically captured under the optical lattice potential. By the spectral analysis of linear stability, we observe that these bright solitons can remain stable across a broad scope of potential parameters, despite the breaking of the corresponding linear PT-symmetric phases.
View Article and Find Full Text PDFPublic Health.
Alzheimers Dement
December 2024
University of California, San Francisco, San Francisco, CA, USA.
Background: Poor sleep health is associated with cognitive impairment (CI) in older adults. The cardiopulmonary coupling (CPC) sleep spectrogram, which estimates the sleep state modulated synchronization between heart rate variability and respiration, is an increasingly recognized measure of sleep stability. However, little is known about the longitudinal association between CPC measures of sleep stability and risk of incident CI.
View Article and Find Full Text PDFStudy of Interfacial Reaction Mechanism of Silicon Anodes with Different Surfaces by Using the In Situ Spectroscopy Technique.
ACS Appl Mater Interfaces
January 2025
Research Center of Nano Science and Technology, College of Sciences, Shanghai University, Shanghai 200444, China.
The interfacial reaction of a silicon anode is very complex, which is closely related with the electrolyte components and surface elements' chemical status of the Si anode. It is crucial to elucidate the formation mechanism of the solid electrolyte interphase (SEI) on the silicon anode, which promotes the development of a stable SEI. However, the interface reaction mechanism on the silicon surface is closely related to the surface components.
View Article and Find Full Text PDFDynamic biomechanical effects of medial meniscus tears on the knee joint: a finite element analysis.
J Orthop Surg Res
January 2025
Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical Engineering, Beihang University, Beijing, 100083, China.
Background: Meniscus tears can change the biomechanical environment of the knee joint and might accelerate the development of osteoarthritis. The aim of this study was to investigate the dynamic biomechanical effects of different medial meniscus tear positions and tear gaps on the knee during walking.
Methods: Seven finite element models of the knee joint were constructed, including the intact medial meniscus (IMM), radial stable tears in the anterior, middle, and posterior one-third regions of the medial meniscus (RSTA, RSTM, RSTP), and the corresponding unstable tears (RUTA, RUTM, RUTP).
Tissue-Adhesive and Stiffness-Adaptive Neural Electrodes Fabricated Through Laser-Based Direct Patterning.
Small Methods
January 2025
Department of Electrical and Computer Engineering, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
Recently, implantable devices for treating peripheral nerve disorders have demonstrated significant potential as neuroprosthetics for diagnostics and electrical stimulation. However, the mechanical mismatch between these devices and nerves frequently results in tissue damage and performance degradation. Although advances are made in stretchable electrodes, challenges, including complex patterning techniques and unstable performance, persist.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!