LABORATORY J.A. DIEUDONNE UMR CNRS-UNS N°6621

Pascal Chossat                          Research Director, CNRS

Address : Laboratoire J.A.Dieudonné UMR CNRS-UNS N°6621 Université de Nice Sophia-Antipolis Parc Valrose 06108 NICE Cedex 2

Phone Number : 04 92 07 XX XX Fax Number : 04 93 51 79 74 Mail : pascal.chossat@unice.fr

My main theme of scientific research is Equivariant Bifurcation Theory, a mathematical approach to the problems of spontaneous symmetry-breaking, pattern selection and dynamics of nonlinear systems which inherit from their basic physical set-up a certain amount of symmetry. This theory has met big successes in understanding and predicting pattern formation and time evolution of some classical hydrodynamical systems, especially the Couette-Taylor problem (onset of structures for a fluid flow set between two rotating cylinders, see P. Chossat et G. Iooss 1994) and the Bénard problem (onset of convective structures). Its applications extend to many other areas of Science, from Biology to Mechanical Systems with symmetry.
It provides a theoretical framework which unifies such phenomena as diverse as patter formation in convective cells of fluide flow and patterns on the coat of zebras or leopards (for example). It allow for a rogorous mathematical approach of dynamical (temporal) phenomena such as intermittency in convective patterns of rotating fluid. 

A comprehensive exposition of the theory can be found in my book with Reiner Lauterbach, here.

Since 2015 I am a member of the project Mathneuro from Inria, for the modelisation of sequential processes in biological neural networks. I study how the cortex produces sequences of memorized actions or concepts, depending on the type of learning and dynamical properties of synapses. To this aim, I rely on a neuronal model equation which I developed with Martin Krupa in 2015, bio-inspired but having geometrical properties which simplify considerably the analysis of existenc of heteroclinic and excitable chains in the network.

My main contributions can be divided into the following domains:

• Bifurcations in systems with planar, cylindrical, spherical or hyperbolic symmetries
• General theory f equivariant bifurcation
  
• Symmetric chaos and attractors
• Bifurcation and stability of robust heteroclinic cycles forced by symmetry
• Method of orbit space reduction for equivariant dynamical systems
• Instabilities and intermittency in the dynamo problem
• Bifurcations in Hamiltonian systems with symmetry
• Neural networks
  

• 2001-2005: Scientific counsellor at the French Embassy in New Delhi
• 2005-2010: Director of the Centre International de Rencontres Mathématiques (International Center for Mathematical Meetings, Luminy)
• 2009-2012: PI of the European project New Indigo (geographic EraNet with India)
• 2009-2012: Deputy Scientific Director of Institut des Mathématiques et leurs Interactions of CNRS
• 2012-2016: Director of the Network of laboratories W. Döblin, FR 2800 CNRS-UniCA
  
• 2012-2016: Member of the Steering Board of the Indo-French Centre in Applied Mathematics
• 2016-2017: In charge of the build up of the Academy of Complex Systems, University Côte d'Azur (UniCA)
  

Books

• P. Chossat, G. Iooss. The Couette-Taylor Problem, Applied Math Science 102, Springer, New-York (1994).
• P. Chossat. proceedings of the ARW "Dynamical Systems, Bifurcation and Symmetry, new trends and new tools" (Cargèse 1993), Kluwer ASI series 437 (1994).
• P. Chossat. Les Symétries Brisées, coll. Sciences d'Avenir, éd. Pour-la-Science - Belin, Paris (1996).
• P. Chossat, R. Lauterbach. Methods in Equivariant Bifurcation and Dynamical Systems, Advanced Series in Nonlinear Dynamics 15, World Scientific, Singapour (2000).

Papers (since 2001)

• P. Chossat. The bifurcation of heteroclinic cycles in systems of hydrodynamical type J. of Continous, Discrete & Impulsive Systsems (2201).
• P. Chossat, J-P Ortega and T. Ratiu. Hamiltonian Hopf Bifurcation with Symmetry Arch. Rational Mech. Anal. 163 (2002) 1-33.
• P. Chossat. The reduction of equivariant dynamics to the orbit space of a compact group action Acta Applicandae Mathematicae, 70 (2002) 71-94.
• P. Chossat and D. Armbruster.Dynamics of polar reversals in spherical dynamos Proc. R. Soc. Lond. A (2002) 458, 1-20.
• P. Chossat, D. Lewis, J-P Ortega and T. Ratiu. Bifurcation of relative equilibria in mechanical systems with symmetryAdvances in Applied Math, 31. (2003) 10-45.
• P. Chossat. A short introduction to bifurcation theory with symmetry and its applications, Microwave measurement Techniques and Appl. J. Behari ed (2003) AnamayaPublishers, New Delhi, India.
• P. Chossat An introduction to equivariant bifurcation and spontaneous symmetry breaking, Peyresq lectures on nonlinear phenomena II, J-A Sépulchre &J-L Beaumont  éd. World Scientific (2003)
• P. Chossat. Stability and Bifurcation from Relative Equilibria and Relative Periodic Orbits, Dynamics and Bifurcation of Patterns in Dis-
  sipative Systems, G. Dangelmayr & I. Oprea  éd., World Scientific Series on Nonlinear Science, Series B Vol. 12 (2004).
  
• P. Chossat and N. Bou-Rabee. The motion of the spherical pendulum subjected to a D_n symmetric perturbation, SIADS, 4, 4, 1140-1158 (2005).
• P. Chossat. La complexité dans la Nature et les brisures spontanées de symétrie, in "Symétries, brisures de symétries et complexitéen mathématiques, physique et biologie. Essais de philosophienaturelle", L. Boi éd, Peter Lang (2006).
• P. Chossat. Une remarque sur les bifurcations avec une singularité quadratique pour lessystèmes O(3) invariants, Comptes-Rendus de l'Académie des Sciences de Paris, Vol.344, 8, 529-533 (2007).
• P. Chossat, O. Faugeras. Hyperbolic planforms in relation to visual edges and textures perception, Plos Computational Biology (2009).
• P. Chossat, G. Faye and O. Faugeras. Bifurcation of Hyperbolic Planforms, J. Nonlinear Science (2011) open access.
• G. Faye, P. Chossat and O. Faugeras. Analysis of a hyperbolic geometric model for visual texture perception, Journal of Mathematical Neuroscience, open access (2011).
• G. Faye and P. Chossat. Bifurcation diagrams and heteroclinic networks of octagonal H-planforms, J. of nonlinear Science, 22, 1 (2012).
• G. Faye, J. Rankin & P. Chossat. Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameteranalysis. J. of Mathematical Biology, Online First (Avril 2012).
• G. Faye and P. Chossat. A spatialized model of visual texture perception using the structure tensor formalism. J. Networks and Heterogeneous Media, Special Issue "Nonlinear Partial DifferentialEquations: Theory and Applications to Complex Systems" (2013).
• O. Podvigina, P. Chossat. Simple heteroclinic cycles in R4. Nonlinearity 28(4) (2015).
• P. Chossat, M. Krupa. Heteroclinic cycles in Hopfield networks. J. of Nonlinear Science, 26, 2 (2016).
• O. Podvigina, P. Chossat. Asymptotic stability of pseudo-simple heteroclinic cycles in R4. J. of Nonlinear Science 27, 1 (2017).
• P. Chossat, M. Krupa. Consecutive and non-consecutive heteroclinic cycles in Hop- field networks. Dynamical Systems 32 1 (2017): Equivariance and Beyond, M. Golubitsky’s 70th birthday.
• C. Aguilar, P. Chossat, M. Krupa, F. Lavigne. Latching dynamics in neural networks with synaptic depression. PLoS ONE, Public Library of Science, 12 (8) (2017)
• E. Köksal Ersöz, C. Aguilar, P. Chossat, M. Krupa, F. Lavigne. Neuronal mecha- nisms for sequential activation of memory items: Dynamics and reliability. PLoS ONE, Public Library of Science, 15 (4), pp.1-28 (2020).
• P. Chossat. The hyperbolic model for edge and texture detection in the primary visual cortex. J. of Mathematical Neuroscience, 10 (2) (2020).
• E. Köksal Ersöz, P. Chossat, M. Krupa, F. Lavigne. Dynamic branching in a neural network model for probabilistic prediction of sequences. J. of Comp. Neuroscience, volume 50, pages 537–557, (2022).
• E. Köksal Ersöz, P. Chossat, F. Lavigne. Gain modulation of actions selection without synaptic relearning. 2024 〈hal-04418804v2〉

Novel

• L'affaire Kalippam (a novel inspired by my four years stay in India): here

Videos

• Spatio-temporal patterns associated with heteroclinic cycles in problems with spherical mode interaction l=3 et 4 (paper Chossat-Beltrame 2015 above): 

        1. Heteroclinic cycle in the case of Fig. 10
        2. Heteroclinic cycle in the case of Fig. 11
        3. Heteroclinic cycle in the case of Fig. 12