Institut de Mathématiques de Toulouse

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Séminaire Mathématiques pour la biologie

par Fanny Delebecque, Pierre Neuvial - publié le , mis à jour le

Organisateurs Fanny Delebecque et Pierre Neuvial
Horaire habituel Jeudi 14h30
Lieu habituel Salle de conférence MIP, (bâtiment 1R3, 1er étage)

  • Jeudi 26 avril 13:30-14:30 - ANNULÉ (Maxime Breden - TU Munich)


    Résumé : About the equilibria of a cross-diffusion system in population dynamics
    Cross-diffusion is a mechanism used in population dynamics to model a repulsive effect between individuals. Mathematically, this corresponds to adding a nonlinear diffusion term to classical reaction-diffusion systems. Cross-diffusion allows to obtain a richer variety of solutions, whose qualitative behavior seems to better fit observations (spatial segregation phenomenon), but it also complicates the mathematical study of these solutions.
    In this talk, I explain how numerical simulations can be combined with a posteriori estimates, to obtain computer-assisted proofs about inhomogeneous steady states of a cross-diffusion system.

    Lieu : salle MIP, 1er étage bat 1R3

  • Jeudi 17 mai 13:30-14:30 - Susely Figueroa (IMT)

    Long time evolutionary dynamics of phenotypically structured populations in time periodic environments

    Résumé : I will present a study of the long time behavior of a parabolic Lotka-Volterra type equation considering a time-periodic growth rate with non-local competition. Such equation describes the dynamics of a phenotypically structured population under the effect of mutations and selection in a time-periodic fluctuating environment. We first prove that, in long time, the solution converges to the unique periodic solution of the problem. Next, we describe this periodic solution asymptotically as the effect of the mutations vanish by using a theory based on Hamilton-Jacobi equations with constraint, proving that the solution concentrates on a single Dirac mass, while the size of the population varies periodically in time. When the effect of the mutations are small but nonzero, we provide some formal approximations of the moments of the population’s distribution. As an application we show, via some examples, how such results could be compared to biological experiments.

    Lieu : salle MIP, 1er étage bat 1R3

  • Jeudi 31 mai 13:30-14:30 - Clément Sire - LPT, IRSAMC

    (Measuring) Social Interactions and (Studying) Collective States in Fish Schools

    Résumé : The flexible coordination of individuals’ movements ensures rapid and coherent changes in direction of travel of fish schools for instance as a reaction to a predator detected in the neighborhood. However the ’microscopic level’ interaction rules involved in the coordination of fish movements and the adapted collective response of a school still remain to a large extent unknown. Knowing such interaction rules could offer new sources of inspiration to design distributed control algorithms for swarms of drones. Here we present a systematic methodology to measure and analyze social interactions controlling the collective motion of animal groups. Contrary to classical forces between physical objects, social interactions between individuals explicitly depend on their relative headings and are affected by their anisotropic and asymmetric perception of their environment. Hence they strongly break the Newtonian’s law of action-reaction. When applied to fish groups, this approach leads to the quantitative measurement of the spontaneous behavior of a fish, of its avoidance interaction with the tank walls, and of its attraction and alignment interaction with another fish. We use the results of this analysis to build an explicit and faithful model that convincingly reproduces quantitative and qualitative features of the actual fish dynamics. We also show that the type of models derived from such analysis reproduces the main collective states observed in actual fish schools, when one varies the intensity of the alignment and attraction interactions between fish.

  • Jeudi 14 juin 13:30-14:30 - Philippe Saint-Pierre - IMT


    Lieu : salle 106 1er étage bat 1R1

    Notes de dernières minutes : Attention, changement de salle : salle 106 1er étage bat 1R1

  • Jeudi 28 juin 14:30-15:30 -