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/index.php/includes/xml/dist/javascript/overlib/skelato/plugins/dw2/IMG/siteon0.gif
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802131979 Gilpin's predatorprey model
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article254
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/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 (...)

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An NMR view of nonlinear magnetization dynamics : in liquid and solid, at low and high polarizations
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article253
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/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 (...)

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Governing equations and topology extracted from observational time series in environmental sciences
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article252
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/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 (...)

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A new class of Ansatz library for nonautonomous systems
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article251
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/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 (...)

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The templex approach in Lagrangian analysis
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article250
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/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, (...)

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Similarities and differences between the control theory for discrete and continuous time chaotic systems
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article249
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/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 (...)

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Numerical approaches for investigating the chaotic behavior of multidimensional Hamiltonian systems
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article248
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article24820231015T06:46:35Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />We discuss various numerical approaches for studying the chaotic dynamics of multidimensional Hamiltonian systems, focusing our analysis on the chaotic evolution of initially localized energy excitations in the disordered KleinGordon oscillator chain in one spatial dimension.

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Hopflike bifurcation in mixed mode oscillation in a fractionalorder FitzHughNagumo model
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article247
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article24720231014T16:26:51Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />Since two decades, Fractional Differential Equations (FDE) are more and more used to model a large variety of phenomena in the nature. Their ability to model better than Ordinary Differential Equations (ODE) is due in particular to the ‘memory' of the initial conditions. The counterpart of this ‘memory' is that FDE cannot exhibit exact periodic solutions and hence Hopf bifurcation. However, in some situations numerical simulations show similarities with such (...)

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On topological synchronization of Rössler systems
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article246
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article24620231014T16:09:39Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />We consider a master/slave system of two interacting almost identical Rössler oscillators], in order to illustrate the concept of topological synchronization. This is a physical concept, which also garnered some press attention, established with the purpose to explain the numerically observed phenomenon where the attractors of the components of a coupled dynamical system becomes very similar as the strength of the coupling is increased, and which is believed to be at the heart of (...)

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Multistability in the spinorbit dynamics of celestial bodies
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article245
http://atomosyd.net/spip.php/local/cachetex/skelato/ecrire/ecrire/ecrire/ecrire/spip.php?article24520231014T16:00:35Ztext/htmlfrLetellierOtto chaos abstracts
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Abstract <br />Mercury and many natural satellites in the Solar System, including the Moon, are currently in a spinorbit resonance, a state where their rotational and orbital periods are commensurable. In this work, we visually illustrate the rich dynamical scenario leading to captures into spinorbit resonances and quasiperiodic attractors in the twobody problem with tidal

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