Search results for "DYNAMICAL SYSTEMS"
showing 10 items of 476 documents
Partially hyperbolic diffeomorphisms with a uniformly compact center foliation: the quotient dynamics
2016
We show that a partially hyperbolic$C^{1}$-diffeomorphism$f:M\rightarrow M$with a uniformly compact$f$-invariant center foliation${\mathcal{F}}^{c}$is dynamically coherent. Further, the induced homeomorphism$F:M/{\mathcal{F}}^{c}\rightarrow M/{\mathcal{F}}^{c}$on the quotient space of the center foliation has the shadowing property, i.e. for every${\it\epsilon}>0$there exists${\it\delta}>0$such that every${\it\delta}$-pseudo-orbit of center leaves is${\it\epsilon}$-shadowed by an orbit of center leaves. Although the shadowing orbit is not necessarily unique, we prove the density of periodic center leaves inside the chain recurrent set of the quotient dynamics. Other interesting proper…
On the thermodynamic origin of metabolic scaling
2018
The origin and shape of metabolic scaling has been controversial since Kleiber found that basal metabolic rate of animals seemed to vary as a power law of their body mass with exponent 3/4, instead of 2/3, as a surface-to-volume argument predicts. The universality of exponent 3/4 -claimed in terms of the fractal properties of the nutrient network- has recently been challenged according to empirical evidence that observed a wealth of robust exponents deviating from 3/4. Here we present a conceptually simple thermodynamic framework, where the dependence of metabolic rate with body mass emerges from a trade-off between the energy dissipated as heat and the energy efficiently used by the organi…
Darboux integrable system with a triple point and pseudo-abelian integrals
2016
We study pseudo-abelian integrals associated with polynomial perturbations of Dar-boux integrable system with a triple point. Under some assumptions we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-abelian integrals is bounded uniformly for nearby Darboux integrable foliations.
A Hybrid Control Strategy for Quadratic Boost Converters with Inductor Currents Estimation
2020
International audience; This paper deals with a control strategy for a DC-DC quadratic boost converter. In particular, a hybrid control scheme is proposed to encompass a control law and an observer for the estimation of the system states, based only on the measurements of the input and output voltages. Differently from classical control methods, where the controller is designed from a small-signal model, here the real model of the system is examined without considering the average values of the discrete variables. Using hybrid dynamical system theory, asymptotic stability of a neighborhood of the equilibrium point is established, ensuring practical stability of the origin, which contains es…
A deeper look into natural sciences with physics-based and data-driven measures
2021
Summary With the development of machine learning in recent years, it is possible to glean much more information from an experimental data set to study matter. In this perspective, we discuss some state-of-the-art data-driven tools to analyze latent effects in data and explain their applicability in natural science, focusing on two recently introduced, physics-motivated computationally cheap tools—latent entropy and latent dimension. We exemplify their capabilities by applying them on several examples in the natural sciences and show that they reveal so far unobserved features such as, for example, a gradient in a magnetic measurement and a latent network of glymphatic channels from the mous…
Attraction in n ‐dimensional differential systems from network regulation theory
2018
On a Planar Dynamical System Arising in the Network Control Theory
2016
We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.
Inferring causation from time series in earth system sciences
2019
The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers.
New Approach of Controlling Cardiac Alternans
2018
The alternans of the cardiac action potential duration is a pathological rhythm. It is considered to be relating to the onset of ventricular fibrillation and sudden cardiac death. It is well known that, the predictive control is among the control methods that use the chaos to stabilize the unstable fixed point. Firstly, we show that alternans (or period-2 orbit) can be suppressed temporally by the predictive control of the periodic state of the system. Secondly, we determine an estimation of the size of a restricted attraction's basin of the unstable equilibrium point representing the unstable regular rhythm stabilized by the control. This result allows the application of predictive control…
Multiple steady states and the form of response functions to antigen in a model for the initiation of T cell activation
2017
The aim of this paper is to study the qualitative behaviour predicted by a mathematical model for the initial stage of T-cell activation. The state variables in the model are the concentrations of phosphorylation states of the T-cell receptor (TCR) complex and the phosphatase SHP-1 in the cell. It is shown that these quantities cannot approach zero and that the model possesses more than one positive steady state for certain values of the parameters. It can also exhibit damped oscillations. It is proved that the chemical concentration which represents the degree of activation of the cell, that of the maximally phosphorylated form of the TCR complex, is, in general, a non-monotone function of…