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/spip.php/overlib/dist/IMG/siteon0.gif
http://www.atomosyd.net/
802132018
http://atomosyd.net/spip.php/dist/spip.php?article198
http://atomosyd.net/spip.php/dist/spip.php?article19820180228T14:52:23Ztext/htmlfrPapers
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C. Letellier, I. SendiñaNadal, E. BiancoMartinez & M. S. Baptista <br />A symbolic networkbased nonlinear theory for dynamical systems observability <br />Scientific Reports, 8, 3785, 2018. <br />Abstract <br />When the state of the whole reaction network can be inferred by just measuring the dynamics of a limited set of nodes the system is said to be fully observable. However, as the number of all possible combinations of measured variables and time derivatives spanning the reconstructed state of the (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique13" rel="directory">Papers</a>
1987 The Ikeda delay differential equation
http://atomosyd.net/spip.php/dist/spip.php?article197
http://atomosyd.net/spip.php/dist/spip.php?article19720180106T17:22:52Ztext/htmlfrLetellierHigher dimensional flows
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Kensuke Ikeda proposed a model of a passive optical resonator system . When the system is an optical bistable resonator, Ikeda and Kenji Matsumoto showed that the dynamics can be reproduced with the single delay differential equation <br />For μ = 16 and x0 = π/3, δt = 0.002 and x(0)=2.5, the chaotic attractor shown in Fig. 1 is obtained. These parameter values were obtained by looking for a simple attractor starting from those provided by (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique6" rel="directory">Higher dimensional flows</a>
1984 A piecewise system for quasiperiodic and chaotic motions
http://atomosyd.net/spip.php/dist/spip.php?article196
http://atomosyd.net/spip.php/dist/spip.php?article19620171118T15:53:34Ztext/htmlfrLetellier3D flows
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When b=0, this system is conservative and produces quasiperiodic motions as evidenced in the Poincaré section defined by y=0 and shown in Fig. 1. Using x0 = 0.1417, y0=z0=0, there is most likely a weakly chaotic toroidal motion (shown in green in Fig. 1.).

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique5" rel="directory">3D flows</a>
1974 : The Pylkin attractor
http://atomosyd.net/spip.php/dist/spip.php?article195
http://atomosyd.net/spip.php/dist/spip.php?article19520171106T20:00:51Ztext/htmlfrLetellierDiscrete maps
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A Plykin attractor is a limit set for a map defined  initially defined on a plane in the spirit of Smale's horseshoe by Romen Vasil'evich Plykin . As reported in , "Plykin also showed that the complement of a connected 1dimensional basic set of the diffeomorphism of the 2sphere consists of at least four connected components (the Plykin attractor has precisely four components in its complement), each containing at least one periodic attracting or repelling point. The Plykin (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique7" rel="directory">Discrete maps</a>
1986 The NoséHoover system (Sprott A system)
http://atomosyd.net/spip.php/dist/spip.php?article193
http://atomosyd.net/spip.php/dist/spip.php?article19320170719T18:37:31Ztext/htmlfrLetellier3D flows
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Shūichi Nosé and by William Hoover , investigated a system of N particles (d degrees of freedom) in a given volume V and interacting (heat transfer) with an external system in such a way that the energy E is conserved. The equations governing the coordinates Q, the momentum P and the effective mass s, after a coordinate transformation, were <br />which were rediscovered by Julian Clinton Sprott as the Sprott A system. This system is a conservative system as shown by its Jacobian (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique5" rel="directory">3D flows</a>
2015 Deterministic approach of cancer dynamics : toward an individualization of pronostic for cancer evolution
http://atomosyd.net/spip.php/dist/spip.php?article192
http://atomosyd.net/spip.php/dist/spip.php?article19220170428T14:52:36Ztext/htmlfrVIGERPh'D Thesis
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Abstract <br />Currently, most research in oncology involve genetic mutations potentially responsible for cancer initiation. Since the identification of a large number of genes involved in carcinogenesis is not correlated to an increase in number of patients in remission, investigating a cancer as a pure genetic process was not effecient as initially expected. Although genetic mutations have a key role in tumorigenesis, some other factors such as the microenvironment should be also (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique27" rel="directory">Ph'D Thesis</a>
2003 A simple model for spiking neurons
http://atomosyd.net/spip.php/dist/spip.php?article191
http://atomosyd.net/spip.php/dist/spip.php?article19120170416T03:28:43Ztext/htmlfrLetellierBiological models
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Eugene M. Izhikevich presented a model that reproduces spiking and bursting behavior of known types of cortical neurons . The model combines the biologically plausibility of the dynamics underlying the Hodgkin–Huxley model and the computational efficiency of integrateandfire neurons. As initiated by Bard Ermentrout and Nancy Kopell , this model is made of an oscillator producing slow oscillations combined with a switching mechanism for reproducing the bursting phenomenon . (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique36" rel="directory">Biological models</a>
2003 A 3D hostimmunetumor system
http://atomosyd.net/spip.php/dist/spip.php?article188
http://atomosyd.net/spip.php/dist/spip.php?article18820170414T18:00:13Ztext/htmlfrLetellierBiological models
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Recent advances in oncology lead to promote the role of the tumor microenvironment in tumor growth . In fact, mathematical cancer model taking into account normal (healthy) cells  thus the microenvironment  interacting with immune and tumor cells are not numerous. There is one proposed by Owen and Sherratt which remains mainly focused on tumor–macrophage interactions, the normal cells being only considered for their ability to colonize the site studied. One of the most (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique36" rel="directory">Biological models</a>
2017
http://atomosyd.net/spip.php/dist/spip.php?article190
http://atomosyd.net/spip.php/dist/spip.php?article19020170414T07:19:39Ztext/htmlfrPapers
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C. Letellier, S. K. Sasmal, C. Draghi, F. Denis & D. Ghosh, <br />A chemotherapy combined with an antiangiogenic drug applied to a cancer model including angiogenesis, <br />Chaos, Solitons & Fractals, 99, 297311, 2017. Onine <br />Abstract <br />Combined therapy made of a chemotherapy and antiangiogenic agents is a clinical treatment recommended for its efficiency. Since the optimization of a treatment against cancer relasp is still mostly based on oncologist's knowhow, it is (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique13" rel="directory">Papers</a>
The driven van der Pol equation
http://atomosyd.net/spip.php/dist/spip.php?article189
http://atomosyd.net/spip.php/dist/spip.php?article18920170412T12:40:51Ztext/htmlfrLetellierDriven systems
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There are many versions for the ``van der Pol'' equation. Among them, there is this one, involving the cubic term, which reads <br />$ \left\ \beginarraylcl \dotx &=& y\\ \doty &=& \mu (1\gamma x^2)y x^3+u \\ \dotu &=& v \\ \dotv &=& \omega^2 u \, . \endarray \right. $ <br />and which was investigated in details in . This is sstem is a semiconservative system which means that there is a continuum of attractors, that is, many many different attractors coexist in the state space . (...)

<a href="http://atomosyd.net/spip.php/dist/spip.php?rubrique33" rel="directory">Driven systems</a>