We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.91.022906 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Opening up creative resources: towards age-friendly communities through rhizomatic thinking and doing.
Educ Action Res
June 2024
Department of Public Health, Leiden University Medical Center, Leiden, The Netherlands.
Globally, many complex issues, like the ageing population and health inequalities, require attention. People are experimenting to combat these issues in their local contexts through bigger or smaller networks; however, much of the knowledge about these initiatives remains localised and elitist and omits the voices and perspectives of citizens. This article identifies the characteristics of a more horizontal, emergent and plural epistemology to mobilize knowledge.
View Article and Find Full Text PDFRNA velocities and generalizations emerge as powerful approaches for extracting time-resolved information from high-throughput snapshot single-cell data. Yet, several inherent limitations restrict applying the approaches to genes not suitable for RNA velocity inference due to complex transcriptional dynamics, low expression, or lacking splicing dynamics, or data of non-transcriptomic modality. Here, we present GraphVelo, a graph-based machine learning procedure that uses as input the RNA velocities inferred from existing methods and infers velocity vectors lying in the tangent space of the low-dimensional manifold formed by the single cell data.
View Article and Find Full Text PDFAnimals survive in dynamic environments changing at arbitrary timescales, but such data distribution shifts are a challenge to neural networks. To adapt to change, neural systems may change a large number of parameters, which is a slow process involving forgetting past information. In contrast, animals leverage distribution changes to segment their stream of experience into tasks and associate them with internal task abstracts.
View Article and Find Full Text PDFUnderstanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models.
View Article and Find Full Text PDFPurpose: To propose a domain-conditioned and temporal-guided diffusion modeling method, termed dynamic Diffusion Modeling (dDiMo), for accelerated dynamic MRI reconstruction, enabling diffusion process to characterize spatiotemporal information for time-resolved multi-coil Cartesian and non-Cartesian data.
Methods: The dDiMo framework integrates temporal information from time-resolved dimensions, allowing for the concurrent capture of intra-frame spatial features and inter-frame temporal dynamics in diffusion modeling. It employs additional spatiotemporal ($x$-$t$) and self-consistent frequency-temporal ($k$-$t$) priors to guide the diffusion process.
Want 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!