DS0705 - Fondements du numérique

a network for Slow-fast Dynamics applied to the Biosciences – SloFaDyBio

Submission summary

Theoretical research in slow-fast dynamics (also known as singular perturbation theory) advances rapidly and is increasingly making a significant impact in various research areas, in particular in the life sciences (neuroscience, epidemiology, ecology, etc.). For example, the “slow-fast dissection” introduced by John Rinzel (New-York University, USA) in the mid-1980s to understand and classify bursting patterns in excitable cells, has become a classical tool not only in applied mathematics but also in neuroscience. What drives this impact is the observation that multiple-timescale phenomena are ubiquitous in scientific data. For instance, in neuronal electrical activity, hormonal regulation, chemical reactions, turbulent flows and population dynamics. Despite the rapid advances of slow-fast theory, its permeation through the various sciences has brought in novel challenges, which require time and joint efforts to be addressed. Equally, the development of slow-fast theory has been patchy and therefore has left behind a constellation of theoretical questions which remain open. Furthermore, a number of other mathematical and modeling frameworks are now in position to propose different and/or complementary paradigms to represent and understand multiple-timescale phenomena. Indeed, complex multiple-timescale dynamics observed in biological data can be seen as the result of successive transitions (or switches), neither necessarily regular nor necessarily periodic, between different levels of activity of a given system. These transitions can be continuous or discontinuous, they can involve the crossing of thresholds or sudden jumps due to folded invariant manifolds, they can be noise-induced or delay-induced, and they can also have a spatial extension. To date, several mathematical paradigms are known to be able to produce such complicated solutions. It can be slow-fast ordinary differential equations, passage through a chain of saddle attractors, a noise-induced perturbation of a system close to instability, etc. Moreover, the diffusion of such phenomena across multiple spatial scales is also very relevant to applications and interesting as a mathematical problem. The resolution of the above questions and challenges is urgently needed in order to provide a unified framework for understanding complex multiple-timescale biological systems. The main scientific goal that we wish to achieve through this network is to favour interactions between researchers interested in these types of phenomena representing a variety of such paradigms. To this aim, we wish to create a structure for researchers that will focus on slow-fast dynamics and also other paradigms generating complex multiple-timescale time series, in particular, “robust heteroclinic cycles”, “infinite-dimensional and stochastic dynamical systems”, and “piecewise-smooth dynamical systems”. Within this network, these three additional research areas will be emphasized through their relationships with classical slow-fast theory and towards not only new mathematical explorations but also practical interactions with the biosciences, especially with the experimental community. The future network will also serve as medium to aid the training of students that will be working on these topics. Over the last two years, the applicant has convened a number of meetings where he has brought together French researchers as well as key European and international partners. Through the SloFaDyBio initiative, the applicant will use his existing network of collaborators as a platform to transform it into a coherent multi-polar consortium. Then, the principal objective will be the emergence within two years of a large-scale network proposal, to be submitted to a European funding body such as ERC or COST. The ANR grant will provide the required financial resources to drive this emerging slow-fast community towards the common focused goal of writing a European network grant proposal.

Project coordination

Mathieu DESROCHES (Institut National de Recherche en Informatique et Automatique)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.


Inria Paris-Rocquencourt Institut National de Recherche en Informatique et Automatique

Help of the ANR 49,920 euros
Beginning and duration of the scientific project: December 2014 - 24 Months

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