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From the nonlinear dynamical systems theory to observational chaos

Christophe LETELLIER
October 9-11, 2023 - Toulouse
PNG - 259.3 ko

Otto E. Rössler completed his studies in medicine but was never a physician. He spent a post-doc with Konrad Lorenz about socio-biology and cognitive science. He continued with a second post-doc with Robert Rosen with whom he learned to reproduce observed dynamics with differential equations. He then started as an academic by teaching computer programming and computed numerical solutions to the differential equations governing chemical reactions. Otto submitted his first paper on chaos in 1976. The Rössler system quickly became one of the prototypes on which the paradigm of chaos theory is constructed. He also introduced hyperchaos and suggested a classification of chaotic attractors. Otto E. Rössler investigated applications of chaos in various fields : chemistry, heart rhythm, biology, electronics, astrophysics, fluid mechanics... In order to celebrate his contribution to chaos theory for his 80th birthday, this forthcoming conference is devoted to enlightening how chaotic behaviors help to understand the reality of the world in its complexity. Contributions should try to show how the concepts of state space, attractor, first-return maps, Poincaré sections, bifurcations, etc. combined with advanced concepts allow for better views of the possible dynamics produced by simple as well as complex systems. Contributions can be either theoretical, numerical, experimental, observational or historical.

PDF - 4 Mo
The poster

- Main topics
History of chaos
Data analysis
Nonlinear dynamical systems theory
Environmental dynamics (hydrology, epidemiology, oceanography, climatology)
Applications (physics, chemistry, biology, plasma, astrophysics, electronics…)

- Invited speakers

  • Luis A. Aguirre
    Using auxiliary information in model building for nonlinear dynamics : An application in robotics
    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 [1]. In the sequel, examples taken from the field of robotics will be presented where building nonlinear models was found helpful [2] The data are either taken from public repositories \citedata or collected in the laboratory. The model class is multivariate nonlinear autoregressive (NAR) polynomial models. As discussed, structure selection is simplified in the present context. The main difference compared to more standard procedures is the use of auxiliary information about fixed points. This influences the stages of structure selection and of parameter estimation. The final models should be helpful to produce trajectories for robots. Laboratory tests show that the models are helpful Online.
  • Christian Mira
    From Lattes’ results to the notion of focal point. Dim 2 case
  • Lars Folke Olsen
    A biochemical reaction with a plethora of non-linear behaviors
    Biochemical reaction systems, whether taking place \textitin vitro or \textitin vivo, have traditionally been considered to operate at or near a steady-state. 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 steady-state behavior is the peroxidase-oxidase (PO) reaction. This experimental reaction system exhibits a wealth of dynamic behaviors starting from bistability to oscillations to quasiperiodicity and chaos. Chaos was first observed in the PO reaction [3] almost simultaneously with the first observation of chaos in the Belousov-Zhabotinskii reaction [4][. Both studies were inspired by Otto R\"ossler’s seminal paper [5], presenting the first example of chaos in a simple chemical reaction model. In the early PO experiments the parameter region in which chaos occurred was situated between regular periodic oscillations and bursting oscillations. Shortly after the discovery of chaos in the PO reaction a simple 4-variable model of the reaction was proposed [6]. This model, sometimes referred to as the DOP model, contains two positive feed-back loops. It could reproduce the simple and bursting oscillations observed experimentally, but in-between these two extremes only periodic mixed-mode oscillations were found.
  • Louis M. Pecora & Thomas L. Carroll
    Statistics of Attractor Embeddings in Reservoir Computing
    A recent branch of AI or Neural Networks that can handle time-varying 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 the RC dynamics. There are some mathematical advances that move that argument closer to a general theorem. However, for RCs constructed from actual physical systems like interacting lasers or analog circuits, the RC dynamics may not be known well or at all. We present a statistic that can help test for homeomorphisms between a drive system and the RC by using the time series from both systems. This statistic is called the continuity statistic and it is modeled on the mathematical definition of a continuous function. We show the interplay of dynamical quantities (e.g. Lyapunov exponents, Kaplan-Yorke dimensions, generalized synchronization, etc.) and embeddings as exposed by the continuity statistic and other statistics based on ideas from nonlinear dynamical systems theory. These viewpoints and results lead to a clarification of various currently vague concepts about RCs, such as fading memory, stability, and types of dynamics that are useful.
  • Arkady Pikovsky
    From Hamiltonian to dissipative chaos and back : A primer of active particles
    Hamiltonian and dissipative dynamics are two main realms of chaos theory. In this talk, I report on a setup where these two cases interplay [7]. 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 non-trivial Hamilton function). Such an overactive particle can demonstrate chaotic or quasiperiodic dynamics. For an interaction of several particles, one often assumes aligning forces that are dissipative. Now, the collective dynamics becomes dissipative and leads to synchronization of particles. In the synchronous regime, the alignment does not work, and the final dynamics is again Hamiltonian.

- Contribution submission : your abstract should be sent to Christophe Letellier
Deadline for the abstract : June 30, 2023
Notification of acceptance : July 15, 2023
Deadline for the full paper (6 pages) : September 1st, 2023
Proceedings will be provided to each participant at the beginning of the workshop.
LaTeX file style for the abstract and template for the abstract as well as for the full paper.

Zip - 10.4 ko
Style file workshop.cls
LaTeX - 2.1 ko
LaTeX Template

- Honorary President Otto E. Rössler

- Scientific Committee
Luis Antonio Aguirre (Universidade Federal de Minas Gerais, Belo Horizonte, Brazil)
Celso Grebogi (University of Aberdeen, UK)
Jürgen Kurths (Potsdam Institute for Climate Impact Research, Germany)
René Lozi (Université de Nice, France)
Lars F. Olsen (University of South Denmark)
Ulrich Parlitz (Max Planck Institute for Dynamics and Self-Organisation, Biomedical Physics Group, Göttingen, Germany)
Louis M. Pecora Naval Research Laboratory (Maryland, USA)
Arkady Pikovsky (University of Potsdam, Germany)
Denisse Sciamarella (CNRS, Institut Franco-Argentin d’Etudes sur le Climat et ses Impacts, Buenos Aires, Argentina)

- Organizing Committee
Sylvain Mangiarotti (Centre d’Etudes Spatiales de la Biosphère, UPS-CNES-CNRS-IRD-INRAE, Toulouse) To write him
Christophe Letellier (CORIA, Rouen Normandie Université)
Denisse Sciamarella (CNRS, Institut Franco-Argentin d’Etudes sur le Climat et ses Impacts, Buenos Aires, Argentina)

- Registration
Early registration (before July 31, 2023) : Senior 260 € and Ph.D. Student 220 €
Late registration (after August 1st, 2023) : Senior 320 € and Ph.D. Student 280 €

Register now

S’inscrire maintenant

- Location
Salle San Subra
4 Rue San Subra
31300 Toulouse, FRANCE


[1] L. A. Aguirre A bird’s eye view of nonlinear system identification, ArXiv

[2] R. F. Santos, G. A. S. Pereira & L. A. Aguirre, Learning robot reaching motions by demonstration using nonlinear autoregressive models, Robotics and Autonomous Systems, 107, 182-195, 2018. Here

[3] L. F. Olsen & H. Degn, Chaos in an enzyme reaction. Nature, 267, 177-178, 1977.

[4] R. A. Schmitz, K. R. Graziani & J. L. Hudson, Experimental-evidence of chaotic states in Belousov-Zhabotinskii reaction, Journal of Chemical Physics, 67, 3040-3044, 1977.

[5] O. E. Rössler, Chaotic behavior in simple reaction system, Zeitschrift f\"ur Naturforschung A, 31, 259-264, 1976.

[6] L. F. Olsen & H. Degn, Oscillatory kinetics of the peroxidase-oxidase reaction in an open system : Experimental and theoretical studies, Biochimica et Biophysica Acta, 523, 321-334, 1978.

[7] I. Aranson & A. Pikovsky, Confinement and collective escape of active particles, Physical Review Letters, 128, 108001, 2022.


The poster
PDF · 4 Mo
4 - 07/06/23

LaTeX Template
LaTeX · 2.1 ko
212 - 07/06/23

Style file workshop.cls
Zip · 10.4 ko
244 - 07/06/23

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