ATOMOSYD
http://www.atomosyd.net/
Analyse TOpologique et MOdélisation de SYstèmes Dynamiques. ATOMOSYD is an acronym to designate the approach we develop to investigate dynamical systems. We are concerned by the topological analysis, that is, a global approach of the phase portrait, and by the possibility to obtain a set of differential equations from measurements. Our researches are performed in CORIA which belongs to CNRS.frSPIP  www.spip.netATOMOSYDhttp://atomosyd.net/IMG/siteon0.gif
http://www.atomosyd.net/
80213Introduction à la circulation des Fluides Physiologiques (2017)
http://atomosyd.net/spip.php/skelato/spip.php?article186
http://atomosyd.net/spip.php/skelato/spip.php?article18620170206T17:53:41Ztext/htmlfrLetellierBooks
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Les fluides physiologiques servent au transport de molécules impliqués dans le fonctionnement des grands organismes. Par exemple, l'air est apporté aux poumons par la ventilation, le sang diffuse l'oxygène jusqu'aux muscles et extrait les « déchets » comme le dioxyde de carbone pour les éliminer du corps. Ce livre se présente comme une introduction à la mécanique des fluides nécessaire à une première approche de la circulation de fluides physiologiques (mécanique des (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique14" rel="directory">Books</a>
2012 The "cord" attractor
http://atomosyd.net/spip.php/skelato/spip.php?article185
http://atomosyd.net/spip.php/skelato/spip.php?article18520161227T19:19:50Ztext/htmlfrAGUIRRE, Letellier3D flows
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Observability is an important concept (see here for understanding and interpreting results of several problems in nonlinear dynamics, such as analysis, synchronization, and control (see for instance). The reason for this is that the method's performance and the reliability of the results depend on the “measured” variable. The "cord" system is of special interest for at least two reasons : i) It produces an attractor which is not equivalent to any known attractor, and ii) (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique5" rel="directory">3D flows</a>
1978 Decay confinement for parametric instability
http://atomosyd.net/spip.php/skelato/spip.php?article184
http://atomosyd.net/spip.php/skelato/spip.php?article18420161216T15:47:23Ztext/htmlfrLetellierLorenzlike systems
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It is known that one of the mechanisms widely used to limit the intensity of parametrically amplified waves is the transfer of energy from them to waves that are damped in the linear approximation and are produced as a result of decay instability. In the simplest formulation, an investigation of this mechanism leads to the problem of the interaction of three resonantly coupled waves ; this differs from the classical problem in that besides the linear damping, two of these waves possess a (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique29" rel="directory">Lorenzlike systems</a>
2011 A non hyperchaotic but 4D system
http://atomosyd.net/spip.php/skelato/spip.php?article183
http://atomosyd.net/spip.php/skelato/spip.php?article18320161108T19:21:33Ztext/htmlfrLetellierHigher dimensional flows
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In 2011, Liangrui Tang, Lin Zhao, and Qin Zhang proposed a new fourdimensional system <br />$ \left\ \beginarrayl \dotx = a (y x) + yz \\[0.1cm] \doty = b (x+y)  xz \\[0.1cm] \dotz = cx  dz + yw \\[0.1cm] \dotw = ey  fw + xz \, . \endarray \right. $ <br />which produces an interesting attractor for the parameter values as a=55, b=25, c=40, d=13, (e=23, and f=8. Initial conditions can be as x = 0, y = 1, z = 0 and w=1. Two planes projections of the attractor (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique6" rel="directory">Higher dimensional flows</a>
1995 A Rösslerlike oscillator
http://atomosyd.net/spip.php/skelato/spip.php?article182
http://atomosyd.net/spip.php/skelato/spip.php?article18220160328T19:24:48Ztext/htmlfrLetellierChaos in electronic circuits
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In 1995, Thomas Carroll designed an easytobuild electronic circuit for producing chaotic behaviors. He started from the Rössler equations where he replaced the nonlinear term by a piecewise linear function , leading to the system <br />$ \left\ \beginarrayl \dotx=\alpha_x (x+\beta y +\Gamma z) \\[0.1cm] \doty=\alpha_y (\gamma x + (1\delta) y) \\[0.1cm] \dotz=\alpha_z (G(x) +z) \endarray \right. $ where the nonlinearity is the piecewise linear function (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique32" rel="directory">Chaos in electronic circuits</a>
1984 The HindmarshRose system
http://atomosyd.net/spip.php/skelato/spip.php?article181
http://atomosyd.net/spip.php/skelato/spip.php?article18120160310T19:29:08Ztext/htmlfrLetellier3D flows
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To overcome the complexity of the HodgkinHuxley model , Richard FitzHugh introduced a secondorder differential equations which appears to be too simplified . Then James Hindmarsh and Malcom Rose added a third equation to limit the neuron firing and got the model <br />$ \left\ \beginarrayl \dotx = I + bx^2  ax^3 + y  z \\[0.1cm] \doty = c  dx^2  y \\[0.1cm] \dotz = r \left[ \displaystyle s (x  X_c) z \right] \endarray \right. $ where x is the membrane (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique5" rel="directory">3D flows</a>
One Hundred Years of General Relativity
http://atomosyd.net/spip.php/skelato/spip.php?article180
http://atomosyd.net/spip.php/skelato/spip.php?article18020160210T20:32:46Ztext/htmlfrLetellierChapters in Book
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Edited by WeiTou Ni <br />The aim of this twovolume title is to give a comprehensive review of one hundred years of development of general relativity and its scientific influences. This unique title provides a broad introduction and review to the fascinating and profound subject of general relativity, its historical development, its important theoretical consequences, gravitational wave detection and applications to astrophysics and cosmology. The series focuses on five aspects of the theory : (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique34" rel="directory">Chapters in Book</a>
2016
http://atomosyd.net/spip.php/skelato/spip.php?article179
http://atomosyd.net/spip.php/skelato/spip.php?article17920160106T17:46:36Ztext/htmlfrPapers
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S. Mangiarotti, F. Le Jean, M. Huc & C. Letellier <br />Global modeling of aggregated and associated chaotic dynamics <br />Chaos, Solitons & Fractals, 83, 8296, 2016. Online <br />Abstract Spatially distributed systems are rather difficult to investigate due to two distinct problems which can be sometimes combined. First, the spatial extension is taken into account by monitoring the system evolution at different locations. Second, the dynamics cannot always be continuously tracked in time, and segments (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique13" rel="directory">Papers</a>
2015 Comparative study of home ventilator performances and analysis of patientventilator interactions in noninvasive ventilation
http://atomosyd.net/spip.php/skelato/spip.php?article178
http://atomosyd.net/spip.php/skelato/spip.php?article17820151201T17:13:17Ztext/htmlfrFRESNELPh'D Thesis
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Defended on November 24, 2015 <br />Abstract Noninvasive ventilation can be defined as a modality of treatment for chronic respiratory failure. Nowadays, it is sufficiently often prescribed to motivate test bench studies whose objectives are to evaluate and compare ventilator performances. To provide reliable and reproducible assessments, we revisited many aspects of test bench studies and developed a parametric procedure for testing ventilators. We initially focused our attention on the (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique27" rel="directory">Ph'D Thesis</a>
Chaotic seasonal variations of plague in India (18961911)
http://atomosyd.net/spip.php/skelato/spip.php?article177
http://atomosyd.net/spip.php/skelato/spip.php?article17720151129T08:34:01Ztext/htmlfrMangiarottiExperimental data
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A seasonal prevalence in plague epidemic broked out in India during the autumn of 1896 in Bombay. Oscillations with a 3month period were observed during the same season of the year . The original data were gathered every two months (see [1] and with the exception of the first fifteen weeks (on point per week) . The original data were processed to be provided (Fig. 1) with a sampling time equal to 1/16 month . <br />A second set of data are here provided. It corresponds to i) (...)

<a href="http://atomosyd.net/spip.php/skelato/spip.php?rubrique24" rel="directory">Experimental data</a>