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://www.atomosyd.net/spip.php/dist/vignettes/local/cachevignettes/L51xH120/skelato/IMG/siteon0.gif
http://www.atomosyd.net/
80213Taxonomy of chaos
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article258
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25820240204T12:41:36Ztext/htmlfrLetellierTopological Analysis
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Towards a unified description of chaotic attractors using templexes <br />Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine what are the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labelling. Addressing these problems correspond to the development of a dynamical taxonomy, exhibiting the key properties discriminating the variety of chaotic behaviors discussed (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique16" rel="directory">Topological Analysis</a>
2024
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article257
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25720240123T20:57:22Ztext/htmlfrPapers
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Caterina Mosto, Gisela D. Charó, Christophe Letellier, & Denisse Sciamarella <br />Templexbased dynamical units for a taxonomy of chaos <br />Chaos, 34, 113111, 2024. Online <br />Abstract <br />Discriminating different types of chaos is still a very challenging topic, even for dissipative threedimensional systems for which the most advanced tool is the template. Nevertheless, getting a template is, by definition, limited to threedimensional objects, since based on knot theory. To deal with higherdimensional (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique13" rel="directory">Papers</a>
2001 A fourdimensional system with a nontrivial attractor
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article256
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25620231208T06:57:52Ztext/htmlfrLetellierHigher dimensional flows
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Denise Sciamarella and Gabriel Mindlin designed the fourdimensional system <br />from a threedimensional system proposed by Deng For appropriate parameter values as <br />this system produces a chaotic attractor (Fig. 1). A solution to this system was investigated with a cell complex in their work. It was recently revisited in terms of templex <br />From the complex of cells Here, a templex was built and, then, a template constructed as drawn in Fig. (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique6" rel="directory">Higher dimensional flows</a>
Templex : the tool to overstep the barrier of the fourth dimension
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article255
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25520231208T02:46:52Ztext/htmlfrLetellierAlgorithms
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Attractors in threedimensional state space can be described using template through knot theory : unfortunately, knot are all trivial in a 4dimensional space and can no longer be used to discriminate the different type of chaotic attractors. Here, the strategy starts with the construction of a cell complex from a cloud of points in state space and then uses the flow to determine the sequence with which the cells are visited. The topology is described by a directed graph where the nodes (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique25" rel="directory">Algorithms</a>
1979 Gilpin's predatorprey model
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article254
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25420231128T05:27:30Ztext/htmlfrLetellierBiological & chemical models
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In 1976, Michael Gilpin met Robert May and Otto E. Rössler  at the conference organized by the latter with Peter Ortoleva at the New York Academy of Science  where Otto suggested that a Volterra model with three species should provide chaos. Following this suggestion, Gilpin restarted from the work by Richard Vance investigated the simplest threespecies model <br />This model is simple in the sense that the three species are treated in a similar way : they only differ by the values of the (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique36" rel="directory">Biological & chemical models</a>
An NMR view of nonlinear magnetization dynamics : in liquid and solid, at low and high polarizations
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article253
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25320231107T16:58:19Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />In Nuclear Magnetic resonance (NMR), it is well known that the interaction between the magnetization of a sample and the detection circuit in an NMR spectrometer gives rise to nonlinear magnetization dynamics. This phenomenon is commonly termed “radiation damping”). In the context of Dynamic Nuclear Polarization (DNP) experiments at low temperatures ( 4 K), it is possible to achieve very high nuclear spin polarization (typically ∼ 80 − 90%. In such (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique39" rel="directory">Otto chaos abstracts</a>
Governing equations and topology extracted from observational time series in environmental sciences
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article252
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25220231016T11:57:49Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />The global modelling technique aims to extract governing equations from observational time series. In this work, two cases of application are presented to illustrate its potential for environmental sciences, one from single time series in soil ecology, another one from a couple of time series in microclimatology. The topology of the obtained models are analyzed and compared with the GumowskiMira map discovered fifty years ago, and with the hyperchaotic system discovered by Otto (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique39" rel="directory">Otto chaos abstracts</a>
A new class of Ansatz library for nonautonomous systems
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article251
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25120231016T11:51:04Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />The aim of the Ansatz libraries is to retrieve original sets of dynamical equations based on a restricted number of time series. In the previous Ansatz library, autonomous dynamical systems were considered. In the real world, however, it is often necessary to consider forced systems involving external variables. In this study, a new class of forcedAnsatz library is introduced for this (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique39" rel="directory">Otto chaos abstracts</a>
The templex approach in Lagrangian analysis
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article250
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article25020231016T10:44:56Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />Lagrangian analysis is central to understanding how fluid particles are organized in their time evolution. Of particular interest in geophysics are rotating fluids in the presence of a radial temperature gradient, similar to those that control the dynamics of the atmosphere and oceans on a planetary scale. The phenomenon can be studied with the help of simplified kinematic models, such as Shadden's driven double gyre, which simulates oceanic patterns, or the Bickley Jet, (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique39" rel="directory">Otto chaos abstracts</a>
Similarities and differences between the control theory for discrete and continuous time chaotic systems
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article249
http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?article24920231016T07:48:26Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />or linear systems, the basic notions of control theory, such as controllability, observability, detectability and stabilizability, are the same for discretetime and continuoustime systems. The situation is quite different for nonlinear systems such as chaotic systems, particularly due to the lack of continuity for discretetime systems. The first consequence of this discontinuity is the existence of onedimensional discrete autonomous chaotic systems. The differences between the (...)

<a href="http://www.atomosyd.net/spip.php/dist/IMG/overlib/spip.php?rubrique39" rel="directory">Otto chaos abstracts</a>