From the nonlinear dynamical systems theory to observational chaos

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.

Note : 50 years ago, a colloquium was organized in Toulouse by Jean Lagasse et Christian Mira. its title was Discrete maps and their applications. Among the contributors, one may find Boris Chirikov, Vladimir Mel’nikov, Michel Hénon, Joseph Ford... The first picture of the chaotic sea of the standard map was published in the proceedings of this conference.

Numerical simulations of the Mira map reproducing one of the pictures published in the proceedings of the 1973 conference.

The poster (A3 format) announcing the workshop

 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 (40 min + 10 min questions)

• Luis A. Aguirre
  Using auxiliary information in model building for nonlinear dynamics : An application in robotics Abstract

• René Lozi
  Would chaotic dynamical systems be more beautiful if they were useless ? Abstract

• Christian Mira
  From Lattes’ results to the notion of focal point. 2D case Abstract

• Lars Folke Olsen
  Chaos in the peroxidase-oxidase reaction : The DOP model revisited Abstract

• Ulrich Parlitz
  Predicting and controlling complex cardiac excitation waves in the heart Abstract

• Louis M. Pecora & Thomas L. Carroll
  Statistics of Attractor Embeddings in Reservoir Computing Abstract

• Arkady Pikovsky
  From Hamiltonian to dissipative chaos and back : A primer of active particles Abstract

• Denisse Sciamarella
  From the Rössler attractor to the templex Abstract

 Program

Program

 Talks (slides) :

• D. Abergel : An NMR view of nonlinear magnetization dynamics : in liquid and solid, at low and high polarizations
• L. A. Aguirre : Using auxiliary information in model building for nonlinear dynamics : An application in robotics
• J.-P. Barbot : Similarities and differences between the control theory for discrete and continuous time chaotic systems
• G. D. Charo : The templex approach in Lagrangian analysis
• D. Das : Application of fractional chaotic system to explore human gait dynamics
• V. de Oliveira : Multistability in the spin-orbit dynamics of celestial bodies
• T. Gaby : On topological synchronization of Rössler systems
• C. Letellier : Otto E. Rössler 1970-1979
• C. Letellier : A tentative history of conservative chaos
• R. Lozi : Would chaotic dynamical systems be more beautiful if they were useless ?
• R. Lozi : Hopf-like bifurcation in mixed mode oscillation in a fractional-order FitzHugh-Nagumo model
• S. Mangiarotti : Governing equations and topology extracted from observational time series in environmental sciences
• T. Michelitsch : Compartment model with retarded transition rates
• C. Mira : From Lattès’ results to the notion of focal point
• L. F. Olsen : Chaos in the peroxidase-oxidase reaction : The DOP model revisited
• A. Pikovsky : From Hamiltonian to dissipative chaos and back : A primer of active particles
• D. Sciamarella : From the Rössler attractor to the templex
• H. Skokos : Numerical approaches for investigating the chaotic behavior of multidimensional Hamiltonian systems
• M. Tabone : A new class of Ansatz library for non-autonomous systems

 Honorary President Otto E. Rössler

 Scientific Committee
Luis Antonio Aguirre (Universidade Federal de Minas Gerais, Belo Horizonte, Brazil)
Celso Grebogi (University of Aberdeen, UK)
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)

 Graphic designer : Hugues Aroux, Rouen Normandie University

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

 Visiting Toulouse

• About the city

• About its history

• Guided tour