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, patternselection and
dynamics of nonlinear systems which inherit from their basic
physical set-up a certain amount of symmetry. This theory
hasundergone a considerable development since the late seventies. It
has been very successful in understanding and predicting pattern
formationand time evolution of some classical hydrodynamical
systems, especially the Couette-Taylor
problem and the Bénard
problem. Its applications extend to
many other areas of Science, like for example Biology,
Phase Transitions and
Mechanical Systems,.
It is a focal point for the application of
mathematical fields such as geometry, algebra, functional
analysis,dynamical systems. It provides a beautiful theoretical
framework which unifies and classifies natural phenomena as
different as the evolutionof instabilities in rotating fluid flows,
the competition of species in population dynamics and the occurence
of self-oscillationsin certain chemical reactions (like the famous
Belousov-Zhabotinsky experiment).
My main contributions can be divided into the
following domains:
- Pattern selection in systems with planar, cylindrical or spherical symmetries
- Hydrodynamical instabilities
- 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
- Bifurcations in neural field models
I was awarded "prix Berthaud", French Academy of Science, 1993.
I am a member of the team-project Neuromathcomp
(INRIA-UNS-CNRS) since 2011.
- 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, from 2009 to 2012.
- 2012-present: Director of the Network
of laboratories W. Döblin,
FR 2800 CNRS-UNS
- 2012-present: Member of the Steering Board of the Indo-French Centre in Applied Mathematics.
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).
Preprints
- P. Chossat, P. Beltrame. Bifurcation of robust heteroclinic cycles in spherically invariant systems with l =3,4 mode interaction, arXiv:0912.3709v1 (2009).
- P. Chossat, G. Faye. Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane, à paraître J. Dynamics and Differential Equations (2013).
Pictures and videos
- Spatio-temporal patterns associated with heteroclinic cycles in problems with spherical mode interaction l=3 et 4 (paper Chossat-Beltrame above):
2. Heteroclinic cycle in the case of Fig. 11
3. Heteroclinic cycle in the case of Fig. 12
- Example of octagonal Hplanform in the Poincaré disc (paper Chossat-Faye-Faugeras 2011, see other examples in the paper):