Perceived Fatigability: Utility of a Three-Dimensional Dynamical Systems Framework to Better Understand the Psychophysiological Regulation of Goal-Directed Exercise Behaviour

2018 ◽  
Vol 48 (11) ◽  
pp. 2479-2495 ◽  
Author(s):  
Andreas Venhorst ◽  
Dominic Micklewright ◽  
Timothy D. Noakes
Keyword(s):  
Dynamical Systems ◽  
Three Dimensional ◽  
Exercise Behaviour ◽  
Systems Framework

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

Development of mixing and isotropy in inviscid homogeneous turbulence

1982 ◽  
Vol 120 ◽  
pp. 155-183 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Dynamical Systems ◽  
Lower Order ◽  
Stokes System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Fourier Space ◽  
Kolmogorov Entropy ◽  
Navier Stokes Equations ◽  
Constant Energy

We have investigated a sequence of dynamical systems corresponding to spherical truncations of the incompressible three-dimensional Navier-Stokes equations in Fourier space. For lower-order truncated systems up to the spherical truncation of wavenumber radius 4, it is concluded that the inviscid Navier-Stokes system will develop mixing (and a fortiori ergodicity) on the constant energy-helicity surface, and also isotropy of the covariance spectral tensor. This conclusion is, however, drawn not directly from the mixing definition but from the observation that one cannot evolve the trajectory numerically much beyond several characteristic corre- lation times of the smallest eddy owing to the accumulation of round-off errors. The limited evolution time is a manifestation of trajectory instability (exponential orbit separation) which underlies not only mixing, but also the stronger dynamical charac- terization of positive Kolmogorov entropy (K-system).

scholarly journals Three-dimensional forced-damped dynamical systems with rich dynamics: Bifurcations, chaos and unbounded solutions

2015 ◽  
Vol 311-312 ◽  
pp. 25-36 ◽  
Author(s):  
Tomoyuki Miyaji ◽  
Hisashi Okamoto ◽  
Alex D.D. Craik
Keyword(s):  
Dynamical Systems ◽  
Three Dimensional ◽  
Unbounded Solutions

Shape of attractors for three-dimensional dissipative dynamical systems

2000 ◽  
Vol 61 (5) ◽  
pp. 5098-5107 ◽  
Author(s):  
S. Neukirch ◽  
H. Giacomini
Keyword(s):  
Dynamical Systems ◽  
Three Dimensional ◽  
Dissipative Dynamical Systems

Emergence of critical climate states during the Pleistocene

2021 ◽  
Author(s):  
Nicholas Golledge
Keyword(s):  
Dynamical Systems ◽  
Late Pleistocene ◽  
Dominant Frequency ◽  
Climate System ◽  
Ice Age ◽  
Early Pleistocene ◽  
Glacial Cycles ◽  
Pleistocene Climate ◽  
System Nodes ◽  
Systems Framework

<p>During the Pleistocene (approximately 2.6 Ma to present) glacial to interglacial climate variability evolved from dominantly 40 kyr cyclicity (Early Pleistocene) to 100 kyr cyclicity (Late Pleistocene to present). Three aspects of this period remain poorly understood: Why did the dominant frequency of climate oscillation change, given that no major changes in orbital forcing occurred? Why are the longer glacial cycles of the Late Pleistocene characterised by a more asymmetric form with abrupt terminations? And how can the Late Pleistocene climate be controlled by 100 kyr cyclicity when astronomical forcings of this frequency are so much weaker than those operating on shorter periods? Here we show that the decreasing frequency and increasing asymmetry that characterise Late Pleistocene ice age cycles both emerge naturally in dynamical systems in response to increasing system complexity, with collapse events (terminations) occuring only once a critical state has been reached. Using insights from network theory we propose that evolution to a state of criticality involves progressive coupling between climate system 'nodes', which ultimately allows any component of the climate system to trigger a globally synchronous termination. We propose that the climate state is synchronised at the 100 kyr frequency, rather than at shorter periods, because eccentricity-driven insolation variability controls mean temperature change globally, whereas shorter-period astronomical forcings only affect the spatial pattern of thermal forcing and thus do not favour global synchronisation. This dynamical systems framework extends and complements existing theories by accomodating the differing mechanistic interpretations of previous studies without conflict.</p>

scholarly journals The Shallow Cognitive Map Hypothesis: A Hippocampal framework for Thought Disorder in Schizophrenia

2021 ◽  
Author(s):  
Ayesha Musa ◽  
Safia Khan ◽  
Minahil Mujahid ◽  
Mohamady
Keyword(s):  
Dynamical Systems ◽  
Cognitive Mapping ◽  
Cognitive Maps ◽  
Cognitive Map ◽  
Thought Disorder ◽  
Cellular Mechanisms ◽  
Relational Knowledge ◽  
Psychological Theories ◽  
Major Chemical ◽  
Systems Framework

Memories are not formed in isolation. They are associated and organized into relational knowledge structures that allow coherent thought. Failure to express such coherent thought is a key hallmark of Schizophrenia. Here we explore the hypothesis that thought disorder arises from disorganized Hippocampal cognitive maps. In doing so, we combine insights from two key lines of investigation, one concerning the neural signatures of cognitive mapping, and another that seeks to understand lower-level cellular mechanisms of cognition within a dynamical systems framework. Specifically, we propose that multiple distinct pathological pathways converge on the shallowing of Hippocampal attractors, giving rise to disorganized Hippocampal cognitive maps and driving thought disorder. We discuss the available evidence at the computational, behavioural, network and cellular levels. We also outline testable predictions from this framework including how it could unify major chemical and psychological theories of schizophrenia and how it can provide a rationale for understanding the aetiology and treatment of the disease.

COVID-19 ORDER PARAMETERS AND ORDER PARAMETER TIME CONSTANTS OF ITALY AND CHINA: A MODELING APPROACH BASED ON SYNERGETICS

2020 ◽  
Vol 28 (03) ◽  
pp. 589-608 ◽  
Author(s):  
T. D. FRANK
Keyword(s):  
Dynamical Systems ◽  
Compartment Model ◽  
Order Parameters ◽  
Unstable State ◽  
Human Populations ◽  
Time Constants ◽  
Systems Perspective ◽  
Infection Dynamics ◽  
Model Spaces ◽  
Systems Framework

From a dynamical systems perspective, COVID-19 infectious disease emerges via an instability in human populations. Accordingly, the human population free of COVID-19 infected individuals is an unstable state and the dynamics away from that unstable state is a bifurcation. Recent research has determined COVID-19 relevant bifurcation parameters for various countries in terms of basic reproduction ratios. However, little is known about the relevant order parameters (synergetics) of COVID-19 bifurcations and the corresponding time constants. Those order parameters describe directions in compartment model spaces in which infection dynamics initially evolves. The corresponding time constants describe the speed of the dynamics along those directions. COVID-19 order parameters and their time constants are derived within a standard SEIR dynamical systems framework and determined explicitly for two published studies on COVID-19 trajectories in Italy and China. The results suggest the existence of certain relationships between order parameters, time constants, and reproduction ratios. However, the examples from Italy and China also suggest that COVID-19 order parameters and time constants in general depend on regional differences and the stage of the local COVID-19 epidemic under consideration. These findings may help to improve the forecasting of COVID-19 outbreaks in new hotspots around the world.

scholarly journals DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART II: THREE-MANIFOLDS, HEEGAARD SPLITTINGS AND THREE-DIMENSIONAL SYSTEMS

2007 ◽  
Vol 17 (06) ◽  
pp. 2085-2095 ◽  
Author(s):  
YI SONG ◽  
STEPHEN P. BANKS
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Systems Theory ◽  
Topological Structure ◽  
Three Dimensional ◽  
Local System ◽  
Operating Point ◽  
Global Behavior ◽  
Heegaard Splittings

The global behavior of nonlinear systems is extremely important in control and systems theory since the usual local theories will only provide information about a system in some neighborhood of an operating point. Away from that point, the system may have totally different behavior and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on two- and three-manifolds and show that it is possible to obtain systems with "arbitrarily strange" behavior, i.e. arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.

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