Laboratoire de Physique Statistique de l'ENS

Département de Physique - Ecole Normale Supérieure
24, rue Lhomond
75230 Paris Cedex 05 - France

Office: Dc16

For info regarding books, conferences and other activities please refer to reseaux complexes homepage. To access a selection of notes and transparencies. To access CV and publications .

Research interests: Complex Systems Dynamics.

Living systems or social systems can be viewed as complex adaptive systems: They are composed of a large number of elements with intricate interactions which are not identical between several instanciations of the system (say between individual organisms of the same species for instance). Still, a number of their properties remain identical between individuals or equivalent systems. Concepts from statistical physics and non-linear dynamics accounts for these properties. The basic assumption of our approach is the interpretation of organization in real complex systems in terms of the attractors of the dynamics of a formal model system.

Bounded Rationality and Socio-Economic Institutions

Classical economics, especially micro-economics, is based on the hypothesis of agents full rationality and does try to describe organisation phenomena which structure agents interactions. By contrast, social sciences, and some economists try to characterise institutions in connection with cooperation and risk aversion issues.  The following note describes an interpretation of institutions in terms of dynamical attractors of social interactions: this is the framework of our work in economics and environmental sciences.

Market organization

In some sense standard economical theory ignores dynamics and is mostly based on equilibrium. How prices are adjusted or how agents decide to have transactions are supposed to be the output of some mysterious and fast process, refered to as "Walrasian tatonnement". In fact real markets, wether financial markets or everyday life markets where ordinary goods are exchanged display a lot of  organisation in relation to information available to the agents. We worked on market of perishable goods when only private information is available (PostScript file). The case when information is exchanged among agents is more classical among economics studying herd behaviour: we studied several problems associated which this case, including new technologies adoption.
Information Contagion

The simplest models of cultural diffusions, such as new technology adoption or commercial products are inspired from epidemiology. Diffusion is based on a contagion process occuring on the occasion of random encounters. Random encounters result in an S shaped dynamics for the adoption rate. Things get more intricate when one takes into account the existence of social networks which support influence propagation and the fact that some innovation does not benefit equally to all agents. For binary choices, the dynamics is described by the use of inhomogeneous automata networks. When only one neighbour is enough to transmit information, percolation phenomena control the dynamics. When economic adjustments are introduced, self-organised criticality and non gaussian fluctuations are observed. In the case of non-binary opinions, either scalar or vectors, one observes social segregation when information contagion is restricted to close enough opinions.

Sustainable development.

Sustainable development is a field of research concerning the possible transitions from a consumption society to types of societies which do not evolve towards the destruction of their own environment by depleting its resources in the case of fisheries for instance or increasing its pollution. Our group participates to a related EEC funded collaboration on extensive agriculture (project IMAGES). A first manuscript about the dynamics of agri-environmental contracts adoption by farmers is available.

Theoretical Immunology

Jerne networks.

 The basic assumption of Jerne networks is that lymphocytes and immunoglobulines interact via the same mechanisms, namely molecular recognition, as they interact with antigens. The immune response to antigen presentation can then be interpreted as an attractor in the dynamics of a network of a large number of connected entities. The analogy with memories and neural nets brings to the paradigm of an immune network proposed by N.Jerne in the early seventies. (Immunology for physicists)


Mutualistic systems are known to occur in nature , e.g. lichens made of algae and fungus, corals made of polypes and algae, insects and bacteria, rumen and bacteria, legumes and bacteria... Exchanges among partners are beneficial for the species involved, which live together in close association. The benefits can be food, energy, protection and transport (pollination).

The emergence and stability of mutualism constitute a paradox in terms of individual selection of the fittest: since giving food to the other symbiont should be costly for the donor, one expects the donor to be disadvantaged in terms of fitness with respect to a more selfish species, which would not give anything back. We contributed a couple of papers to the hydra-algae symbiosis to study the role of molecular recognition in favoring the emergence of mutualism.