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/overlib/skelato/overlib/skelato/skelato/IMG/siteon0.gif
http://www.atomosyd.net/
80213Predicting and controlling complex cardiac excitation waves in the heart
http://www.atomosyd.net/spip.php?article240
http://www.atomosyd.net/spip.php?article24020230630T13:06:58Ztext/htmlfrLetellierOtto chaos abstracts
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The myocardium is an electrically excitable medium that supports various types of excitation waves, including stable or chaotic spiral waves that cause lifethreatening arrhythmias such as ventricular fibrillation. Developing less invasive lowenergy methods to terminate these arrhythmias requires a deeper understanding of the underlying chaotic spatiotemporal dynamics and novel control methods . Another challenge is the limited experimental and clinical observability of cardiac (...)

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Topological characterization of 3D attractors
http://www.atomosyd.net/spip.php?article239
http://www.atomosyd.net/spip.php?article23920230623T17:01:35Ztext/htmlfrLetellierAlgorithms
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Here are inserted the codes used for completing a topological characterization of a 3D chaotic attractor. The whole procedure is described in a paper which is forthcoming. Most of the code are written in basic C++, some others are in Fortran 90 (thanks to Eduardo Mendes who updated them). As a graphical tool, I am using XmGrace (included in most of the Linux package). The parameter files (*.par) for formatting the figure using this software called by some of the codes are provided. <br />Any (...)

<a href="http://www.atomosyd.net/spip.php?rubrique25" rel="directory">Algorithms</a>
Would chaotic dynamical systems be more beautiful if they were useless ?
http://www.atomosyd.net/spip.php?article238
http://www.atomosyd.net/spip.php?article23820230622T08:48:47Ztext/htmlfrLetellierOtto chaos abstracts
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Since the very beginning of their appearance in the history of humanity, research in mathematics has been guided by two different currents : theory and applications or in other words by beauty and utility. Around 5,000 years ago people in the Mesopotamia and Egypt began using arithmetic, algebra and geometry for commerce, trade, taxation and social activities. Later, in the 6th century BC, Greeks introduced mathematics as a demonstrative discipline. This dual stream of research still (...)

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From Lattès' results to the notion of focal point
http://www.atomosyd.net/spip.php?article237
http://www.atomosyd.net/spip.php?article23720230613T15:36:26Ztext/htmlfrLetellierOtto chaos abstracts
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This contribution is a development of a Note based on Samuel Lattes' paper Published in French, these two papers remained quasi unknown in the contemporary literature. Lattes' contribution describes a method for generating particular families of Dimp nonlinear invertible maps T with vanishing denominators, Such a map have an exceptional property : their inverse T1 is easily obtained and, with an initial condition (x0,x1,..., xp1), the solution xn = g(x0, x1,...,xp1) can be expressed (...)

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Statistics of attractor embeddings in reservoir computing
http://www.atomosyd.net/spip.php?article236
http://www.atomosyd.net/spip.php?article23620230612T13:22:36Ztext/htmlfrLetellierOtto chaos abstracts
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A recent branch of AI or Neural Networks that can handle timevarying signals often in real time has emerged as a new direction for signal analysis. These dynamical systems are usually referred to as reservoir computers. A central question in the operation of these systems is whether a reservoir computer (RC) when driven by only one time series from a driving or source system is internally recreating all the drive dynamics or attractor itself., i.e. an embedding of the drive attractor in (...)

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A biochemical reaction with a plethora of nonlinear behaviors
http://www.atomosyd.net/spip.php?article235
http://www.atomosyd.net/spip.php?article23520230612T13:17:50Ztext/htmlfrLetellierOtto chaos abstracts
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Biochemical reaction systems, whether taking place \textitin vitro or \textitin vivo, have traditionally been considered to operate at or near a steadystate. Now we know that this is not the case, and that biochemical, and more generally biological, systems have natural dynamic behaviors that include oscillations, quasiperiodcity and chaos. A herald of simple (bio)chemical systems NOT showing steadystate behavior is the peroxidaseoxidase (PO) reaction. This experimental reaction system (...)

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Using auxiliary information in model building for nonlinear dynamics : An application in robotics
http://www.atomosyd.net/spip.php?article234
http://www.atomosyd.net/spip.php?article23420230612T13:07:20Ztext/htmlfrLetellierOtto chaos abstracts
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Model building from data consists of a few steps : data collection, choice of model class, structure selection, parameter estimation and model validation. In this talk, after a brief mention of such steps, the main ideas of using auxiliary information will be discussed . In the sequel, examples taken from the field of robotics will be presented where building nonlinear models was found helpful The data are either taken from public repositories \citedata or collected in the laboratory. The (...)

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From Hamiltonian to dissipative chaos and back : A primer of active particles
http://www.atomosyd.net/spip.php?article233
http://www.atomosyd.net/spip.php?article23320230612T13:04:33Ztext/htmlfrLetellierOtto chaos abstracts
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Hamiltonian and dissipative dynamics are two main realms of chaos theory. In this talk, I report on a setup where these two cases interplay. I start with a classical Hamiltonian system of a particle moving in an external potential. Adding activity to the particle motion makes the dynamics dissipative, with a possibility for a strange attractor in the dynamics. However, in the overactive limit, where the activity is very strong, the system is again Hamiltonian (although with a quite (...)

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From the Rössler attractor to the templex
http://www.atomosyd.net/spip.php?article232
http://www.atomosyd.net/spip.php?article23220230612T12:39:42Ztext/htmlfrLetellierOtto chaos abstracts
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Developing methods to accomplish a topological description of the structure of a flow in highdimensional state space (in more than three dimensions) has involved several false starts as well as partially successful roads, that finally lead to what we now call a templex. Cell complexes can be traced back to Poincaré's papers in the late 1800s and the study of chaotic attractors using cell complexes to the 1990s Since then, algebraic topology has been seen as the mathematical (...)

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Computing the structurality
http://www.atomosyd.net/spip.php?article231
http://www.atomosyd.net/spip.php?article23120230420T12:56:40Ztext/htmlfrLetellierAlgorithms
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With Inmaculada Leyva and Irene SendinaNadal, we proposed a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity.[[C. Letellier, I. Leyva & I. SendiñaNadal Dynamical complexity measure to distinguish organized from disorganized dynamics Physical Review E, 101, 022204, 2020. Online] The approach combines two quantities that separately assess the degree of unpredictability of the dynamics and the lack of (...)

<a href="http://www.atomosyd.net/spip.php?rubrique25" rel="directory">Algorithms</a>