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A research group
Articles
Analyse TOpologique et MOdélisation de SYstèmes Dynamiques
ATOMOSYD
News
A Team
1. Christophe LETELLIER
Clément DRAGHI
Fabrice DENIS
Valérie MESSAGER
Collaborations
Luis A. AGUIRRE
Otto E. RÖSSLER
Research Group on Ventilatory Handicap
Robert GILMORE
Publications
Books
1. Le Chaos dans la nature (2006)
2. The Symmetry of Chaos (2007)
3. Introduction à la circulation des Fluides Physiologiques (2011)
5. Topology and Dynamics of Chaos
6. Introduction à la circulation des Fluides Physiologiques (2017)
7. Chaos in Nature (2019)
8. Chaos (2020)
Introduction à la circulation des fluides physiologiques (2022)
Chapters in Book
2002. Modelling and Forecasting Financial Data
2005. Advances in the Applications of Nonstandard Finite Difference Schemes
2007. Progress in Sleep Apnea Research
2013. Chaos, CNN, Memristors and Beyond
2014. Sciences des Sixties
2016. One Hundred Years of General Relativity
Papers
1994
1995
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1997
1998
1999
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2001
2002
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2004
2005
2006
2007
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2010
2011
2012
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2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
Please note
Ph.D. Thesis
1994 Topological characterization and global modeling of chaotic attractors
1999 Nonlinear analysis of dynamics underlying cylindrical liquid jets
2004 Control and diagnosis oriented modelling of the compression ignition engine
2004 Spatio-temporal dynamics in a monomode laser
2005 Asynchronisms in patient-ventilator interactions in noninvasive ventilation
2008 Quality of patient-ventilator interactions in nocturn noninvasive ventilation
2011 Cardio-respiratory follow-up of infatns with sudden death risk
2011 Noise titration for detecting determinism and nonlinearity in dynamics underlying biomedical data
2014 Composition law of branched manifolds for describing chaotic attractors bounded by high-genus torus
2015 Comparative study of home ventilator performances and analysis of patient-ventilator interactions in noninvasive ventilation
2015 Deterministic approach of cancer dynamics : toward an individualization of pronostic for cancer evolution
2015 Modeling the cardio-respiratory system : cardiac remodeling and patient-ventilator interaction
2017 Individualization of predictive models for tumor growth
Research Topics
Bio-Medical Applications
Assessing performances of devices for noninvasive mechanical ventilation
Describing patient-ventilator interactions
Modelling tumor growth and cancer dynamics
Non Invasive Mechanical Ventilation
Nonlinear analysis of cardio-dynamics
Global Modelling & Observability
Observability and Synchronizability
Observability of networks
A symbolic nonlinear theory for network observability
Topological Analysis
Taxonomy of chaos
What Topological Analysis is ?
Teaching
Des particules à l’univers
Histoire des Sciences
Panorama de la Physique Moderne
Algorithms
Articles
Computing a bifurcation diagram
Computing the dynamical complexity
Estimating Shannon Entropy from Recurrence Plots
Estimating the minimum embedding dimension
Fitting polynomials for computing time derivatives
Global Modeling Procedure for R
Templex : the tool to overstep the barrier of the fourth dimension
Topological characterization of 3D attractors
Collaborators
Articles
1. AGUIRRE Luis A.
1. Otto E. RÖSSLER
2. GILMORE Robert
7. MANGIAROTTI Sylvain
8. ROSALIE Martin
MALASOMA Jean-Marc
Experimental data
Articles
Breathing patterns during noninvasive mechanical ventilation
Canadian Lynx counted by the Hudson Bay Company
Chaotic seasonal variations of plague in India (1896-1911)
Copper electrodissolution in phosphoric acid
Covered sunspot data
EEG during noninvasive mechanical ventilation
Homoclinic behavior in the Belousov-Zhabontinski reaction
Patient-ventilator synchronization during non-invasive ventilation
News
Articles
Benoit Mandelbrot : a life for fractals
DYnamique et COntrôle des Croissances TUmorales
Edward N. Lorenz: a butterfly for wheather forecasts
From Laser Dynamics to Topology of Chaos
From Nonlinear Dynamics to BioMedicine
From the nonlinear dynamical systems theory to observational chaos
Georg Duffing : from engineering to nonlinear dynamics
Les ErgoRameurs
Memristor : Past, present & Future
Abstracts
Analysis of a four-state model for tumor growth dynamics and mathematical methods of intervention
Characterization of the effects of bevacizumab on the tumor vascular dynamics to optimize the association anti-VEGF / radiation therapy
Classical mathematical laws for description and prediction of experimental tumor growth
Comparison of three modeling approaches in CEUS studies
DEs, DCs and Doses : Mathematical approaches to designing cancer vaccines
Graph-based mathematical morphology for the characterization of tumor growth in digital pathology
How the growth rate of host cells affects cancer risk in a deterministic way
Mathematical modeling of the microtubule dynamic instabilities
Modeling gene networks : application to the study of cell transformation
Mutli-scale modeling and oxygen impact simulation on temporal evolution of rectum cancer treatment by radiotherapy
Predicting lung tumor evolution during radiotherapy from PET images using a patient specific model
Quantitative models of glioma : from data at the tissue scale to a model of radiotherapy
Spatial avascular growth of tumor in a homogeneous environment
Survival in a phase III randomized trial comparing the “sentinel” web-application versus a standard imaging follow-up for lung cancer patients : first results
Vascular remodeling during radiotherapy
Wavelet-based multifractal analysis of dynamic infrared thermograms and X-ray mammograms to assist in early breast cancer diagnosis
Otto chaos abstracts
A new class of Ansatz library for non-autonomous systems
A tentative history of conservative chaos
An NMR view of nonlinear magnetization dynamics : in liquid and solid, at low and high polarizations
Application of fractional chaotic system to explore human gait dynamics
Chaos in the peroxidase-oxidase reaction : The DOP model revisited
Compartment model with retarded transition rates
From Hamiltonian to dissipative chaos and back : A primer of active particles
From Lattès’ results to the notion of focal point
From the Rössler attractor to the templex
Governing equations and topology extracted from observational time series in environmental sciences
Hopf-like bifurcation in mixed mode oscillation in a fractional-order FitzHugh-Nagumo model
Multistability in the spin-orbit dynamics of celestial bodies
Numerical approaches for investigating the chaotic behavior of multidimensional Hamiltonian systems
On topological synchronization of Rössler systems
Otto Rössler 1970-79 : From chemical reactions To the topology of chaos
Predicting and controlling complex cardiac excitation waves in the heart
Similarities and differences between the control theory for discrete and continuous time chaotic systems
Statistics of attractor embeddings in reservoir computing
The templex approach in Lagrangian analysis
Using auxiliary information in model building for nonlinear dynamics : An application in robotics
Would chaotic dynamical systems be more beautiful if they were useless ?
The challenging systems
A Chua electronic circuit
The 84 Lorenz system
The modified hyperchaotic Rössler system
The Rucklidge system
The Sprott H system
Scientific Mediations
Articles
0. 2004 Exposition : Le chaos dans la nature
1. 2005 La Danse du Chaos
2. 2005 Einstein et la physique du XX
e
siècle naissant
3. 2008 La combustion, qu’est-ce que c’est ?
4. 2009 Johannes Kepler & Galilée : de l’héliocentrisme à une astronomie physique
5. 2012 Henri Poincaré, mathématicien, ingénieur, astronome, philosophe
6. 2013 Le modèle atomique de Bohr
9. 2021 Des découvertes par des scientifiques émotifs
Temps et Mouvement : une dualité incontournable
Some dynamical systems
3D flows
1963 The Lorenz system
1976 The Rössler system
1978 Torn Unimodal Chaos
1980 Nonlinearly coupled waves in plasma
1981 The Burke & Shaw system
1982 A model for plasma instabilities
1984 A 3D model for global atmospheric circulation
1984 A piecewise system for quasi-periodic and chaotic motions
1984 Cord toroidal chaos
1986 The Nosé-Hoover system (Sprott A system)
1987 A normal form for the Belousov-Zhabotinski reaction
1992 The Genesio-Tesi system
1994 Unimodal toroidal chaos
1998 Inverted smooth unimodal chaos
1999 A genus-5 multispiral attractor
1999 A semi-conductor laser driven by a light beam
2007 A 3D symmetrical toroidal chaos
2010 Multi-folded toroidal chaos
2011 Chaotic Blazhko effect in RR Lyrae stars
2012 The "cord" attractor
Lorenz-like systems
1958 A simple model for the earth magnetic field
1972 The Malkus water wheel
1978 Decay confinement for parametric instability
1980 The Shimizu-Morioka system
1981 A possible model for the onset of turbulence
1981 Rigid body-motion with linear feedback
1988 : A chaotic model of El Niño
1990 A model for a simple dynamo system
1992 A model for weakly nonlinear double convection
1992 A thermal convection loop
1999 The "Chen-Ueta" system
Introduction
Biological & chemical models
1979 Gilpin’s predator-prey model
1983 A 4D model for the peroxidase-oxidase reaction
1984 The Hindmarsh-Rose system
2003 A 3D host-immune-tumor system
2003 A simple model for spiking neurons
2016 A 5D tumour-immune-virus system
Chaos in electronic circuits
1915 The Colpitts oscillator
1978 A simple autogenerator of chaotic behaviors
1984 The Chua circuit
1992 The Alpazur oscillator
1995 A Rössler-like oscillator
1995 A Wien-bridge oscillator
Chaotic electronic circuits
Discrete maps
1. The Logistic Map
1968 : A one-dimensional noninvertible map
1973 : The quasi-conservative Gumowski-Mira map
1974 : The Pylkin attractor
1975 : A 2D predator-prey map
4. 1976 : The Hénon map
5. 1978 : The Lozi map
6. 1978 : The Curry-Yorke map
6. 1980 : The Ikeda map
Driven systems
A driven Chen system for a double-torus attractor
The driven van der Pol equation
Higher dimensional flows
1979 The hyperchaotic Rössler system
1987 The Ikeda delay differential equation
2001 A four-dimensional system with a non-trivial attractor
2011 A non hyperchaotic but 4D system
Minimal systems
A first class of minimal chaotic flows
The simplest equivariant jerk system
Rubriques
A research group
Algorithms
Collaborators
Experimental data
News
Scientific Mediations
Some dynamical systems
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