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/skelato/IMG/siteon0.gif
http://www.atomosyd.net/
802132003 A simple model for spiking neurons
http://atomosyd.net/spip.php/spip.php?article191
http://atomosyd.net/spip.php/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/spip.php?rubrique36" rel="directory">Biological models</a>
2003 A 3D hostimmunetumor system
http://atomosyd.net/spip.php/spip.php?article188
http://atomosyd.net/spip.php/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/spip.php?rubrique36" rel="directory">Biological models</a>
2017
http://atomosyd.net/spip.php/spip.php?article190
http://atomosyd.net/spip.php/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/spip.php?rubrique13" rel="directory">Papers</a>
The driven van der Pol equation
http://atomosyd.net/spip.php/spip.php?article189
http://atomosyd.net/spip.php/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/spip.php?rubrique33" rel="directory">Driven systems</a>
2016 A 5D tumourimmunevirus system
http://atomosyd.net/spip.php/spip.php?article187
http://atomosyd.net/spip.php/spip.php?article18720170412T07:39:02Ztext/htmlfrLetellierBiological models
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There are some evidences that oncolytic viruses can be effective in treating cancer. in order to better understand the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumor control or tumor escape, mathematical modelling of cancer oncolytic therapies appears as one possible ways for has been used to investigate the biological mechanisms behind the observed patterns of tumour growth. The mathematical model is here presented to investigate the chaotic (...)

<a href="http://atomosyd.net/spip.php/spip.php?rubrique36" rel="directory">Biological models</a>
Introduction à la circulation des Fluides Physiologiques (2017)
http://atomosyd.net/spip.php/spip.php?article186
http://atomosyd.net/spip.php/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/spip.php?rubrique14" rel="directory">Books</a>
2012 The "cord" attractor
http://atomosyd.net/spip.php/spip.php?article185
http://atomosyd.net/spip.php/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/spip.php?rubrique5" rel="directory">3D flows</a>
1978 Decay confinement for parametric instability
http://atomosyd.net/spip.php/spip.php?article184
http://atomosyd.net/spip.php/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/spip.php?rubrique29" rel="directory">Lorenzlike systems</a>
2011 A non hyperchaotic but 4D system
http://atomosyd.net/spip.php/spip.php?article183
http://atomosyd.net/spip.php/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/spip.php?rubrique6" rel="directory">Higher dimensional flows</a>
1995 A Rösslerlike oscillator
http://atomosyd.net/spip.php/spip.php?article182
http://atomosyd.net/spip.php/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/spip.php?rubrique32" rel="directory">Chaos in electronic circuits</a>