Search results for "dynamical system"
showing 10 items of 523 documents
A posteriori error estimates for Webster's equation in wave propagation
2015
We consider a generalised Webster’s equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster’s equation in generalised form has been rigorously derived in a previous article starting from the wave equation, and it approximates cross-sectional averages of the propagating wave. Here, the approximation error is estimated by an a posteriori technique. peerReviewed
Analyse de la dynamique de la durée du potentiel d'action cardiaque à travers un modèle itératif
2013
International audience; Le présent travail a pour but de caractériser, par une étude mathématique rigoureuse la dynamique du modèle itératif de la durée du potentiel d'action. L'étude de ce modèle, qui découle de celui de Beeler Reuter (BR), se caractérise par une dynamique matérialisée par une courbe de restitution et qui peut servir d'outil pertinent dans l'analyse et le diagnostic d'arythmie. Par ailleurs l'analyse de la stabilité du modèle permet de définir les zones d'existence de différents rythmes cardiaques.
Darboux systems with a cusp point and pseudo-abelian integrals
2018
International audience; We study pseudo-abelian integrals associated with polynomial deformations of Darboux systems having a cuspidal singularity. Under some genericity hypothesis we provide locally uniform boundedness of on the number of their zeros.
Global dynamical behaviors in a physical shallow water system
2016
International audience; The theory of bifurcations of dynamical systems is used to investigate the behavior of travelling wave solutions in an entire family of shallow water wave equations. This family is obtained by a perturbative asymptotic expansion for unidirectional shallow water waves. According to the parameters of the system, this family can lead to different sets of known equations such as Camassa-Holm, Korteweg-de Vries, Degasperis and Procesi and several other dispersive equations of the third order. Looking for possible travelling wave solutions, we show that different phase orbits in some regions of parametric planes are similar to those obtained with the model of the pressure …
Building Anosov flows on $3$–manifolds
2014
We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting both of a transitive Anosov vector field and a non-transitive Anosov vector field; 2. for any n, we build a 3-manifold M supporting at least n pairwise different Anosov vector fields; 3. we build transitive attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive attractors; 4. we build a transitive Anosov vector field admitting infinitely many pairwise non-isotopic trans- verse tori.
Bifurcations in the elementary Desboves family
2017
International audience; We give an example of a family of endomorphisms of $\mathbb{P}^2(\mathbb{C})$ whose Julia set depends continuously on the parameter and whose bifurcation locus has non-empty interior.
Rotation Forms and Local Hamiltonian Monodromy
2017
International audience; The monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article, we give a general approach to the computation of monodromy that resembles the analytical one, reducing the problem to the computation of residues of polar 1-forms. We apply our technique to three celebrated examples of systems with monodromy (the champagne bottle, the spherical pendulum, the hydrogen atom) and to the case of non-degenerate focus-focus singularities, re-obtaining the classical results. An advantage of this approach …
Laminations and tilings of the Hyperbolic upper half plane
2005
This thesis is devoted to the study of dynamical systems associated with tilings of theEuclidean plane or of the Hyperbolic half-plane. A such tiling codes an action of a group ofisometries (namely the group of translations of the plane or the group of affine maps) on a compactmetric space $\Omega$ such that the properties of this action are related with the combinatoricproperties of the tiling. The behaviors of the actions obtained by this way are really various. Insome cases, like for example for the Penrose's tiling, this action is free and minimal. This givesto the set $\Omega$ a structure of a specific lamination called {\it solenoid}. This space islocally the product of a Cantor set w…
Control of the One Dimensional Map Dynamics of the Cardiac Action Potential Duration
2015
International audience; The aim of this work is to investigate the control of the chaos in the one dimensional map which modelizes the duration of the current cardiac action potential (APD) as a function of the previous one. Using OGY control method, we obtain very satisfactory numerical results to stabilize the irregular heart rhythm into the normal rhythm.
Unfolding of saddle-nodes and their Dulac time
2016
Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF. In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle-node and a parameter belonging to a space of functions. In the second part, we apply this first result for proving a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an unfolding of a saddle-node. This result is a b…