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Faculté des arts et des sciences - Département de mathématiques et de statistique

Jacques Bélair

Page de Jacques Bélair Ph.D. (Cornell 1983)
Professeur titulaire
 
MAT1958 - Mathématiques pour chimistes
   

 

Champs d'intérêt et thèmes d'enseignement

La théorie des systèmes dynamiques est utilisée dans la modélisation de systèmes physiologiques en exploitant le concept de maladie dynamique: les bifurcations dans des équations différentielles avec délais sont associées à des dérèglements et/ou des changements qualitatifs dans les comportements des systèmes biologiques, lorsque un ou plusieurs paramètres changent de valeurs. Ces études visent à mieux comprendre l'origine dynamique des dérèglements observés dans ces pathologies, en terme de quelques paramètres accessibles expérimentalement. Nos travaux portent sur la représentation de l'administration et de l'absorption de médicaments, particulièrement dans le contexte de fluctuations dans les concentrations des substances actives, de même que sur la modélisation mathématique elle-même (voir Centre for Nonlinear Dynamics in Physiology and Medicine et Colloque 2004 du Groupe des didacticiens des mathématiques du Québec).

Publications

Articles avec comité de lecture

  • BUONO P.L. & BÉLAIR J., Delay Induced Oscillations in Autonomous Drug Delivery Systems, Journal of Nonlinear Studies, Sous Presse (2004).
  • BERNARD S., BÉLAIR J. & MACKEY M., Bifurcations in a White Blood Cell Production Model, CR Biologie, Sous Presse (2004).
  • BERNARD S., BÉLAIR J. & MACKEY M., Oscillations in Cyclical Neutropenia: New Evidence Based on Mathematical Modeling, Journal of Theoretical Biology, 223, pp. 283-298, 2003.
  • BUONO P.L. & BÉLAIR J., Restrictions and Unfolding of Double Hopt Bifurcations in Functional Differential Equations, Journal of Differential Equations, 189, pp. 234-266, 2003.
  • LEMAIRE V., BÉLAIR J. & HILDGEN P., Structural Modelling of Drug Release from Biodegradable Porous Matrices Based on a Combined Diffusion/Eropsion Process, International Journal of Pharmaceuticals, 258, pp. 95-107, 2003.
  • LAFRANCE P., NEKKA F., VARIN F., LEMAIRE V., DONATI F. & BÉLAIR J., Spatial Effects in Modeling Pharmacokinetics of Rapid Action Drugs, Bulletin of Mathematical Biology, 64, pp. 483-500, 2002.
  • BERNARD S., BÉLAIR J. & MACKEY M., Sufficient Conditions for Stability of Linear Differential Equations with Distributed Delay, Discrete and Continuous Dynamical Systems, 1B, pp. 233-256, 2001.
  • ENGELBORGHS K., LEMAIRE V., BÉLAIR J. & ROOSE D., Numerical Bifurcation Analysis of Delay Differential Equations Arising from Physiological Modeling, Journal of Mathematical Biology, 42, pp. 361-385, 2001.
  • BÉLAIR J. & MAHAFFY J., Variable Maturation Velocity and Parameter Sensitivity in a Model of Haematopoiesis, IMA Journal of Mathematics Applied to Biology and Medicine, 18, pp. 193-211, 2001.
  • 25.01.2008 M., Regulation of Platelet Production: the Normal Response to Perturbation and Cyclical Platelet Disease, Journal of Theoretical Biology, 206, pp. 585-603, 2000.
  • MELANÇON G., JOANETTE Y. & BÉLAIR J., Chaos, Brain and Cognition : Toward a Nonlinear Order, Brain and Cognition, vol.42, pp 33-36, 2000.
  • CAMPBELL S. & BÉLAIR J., Resonant co dimension two bifurcation in the harmonic oscillator with delayed forcing, Canadian Applied Mathematics Quarterly, 7, pp. 217-238, 1999.
  • BÉLAIR J., Stability analysis of an age-structured model with a state-dependent delay, Canadian Applied Mathematics Quarterly, 6, pp. 305-319, 1998.
  • MAHAFFY J., BÉLAIR J. & MACKEY M., Haematopoietic Model with Moving Boundary Condition and State Dependent Delay, Journal of Theoretical Biology, 190, pp. 135-146, 1998.
  • OLIEN L. & BÉLAIR J., Bifurcations, stability, and monotonicity properties of a delayed neural network model, Physica D, 102, pp. 349-363, 1997.
  • RUSTUM C. & BÉLAIR J., Estimation numérique de la vitesse de décroissance des spectres de puissance, Journal of Physics A, 30, pp. 2197-2209, 1997.
  • BÉLAIR J. & DUFOUR S., Stability in a three-dimensional system of delay-differential equations. Canadian Applied Mathematics Quarterly, 4, pp. 136-156, 1996.
  • BÉLAIR J., CAMPBELL S. & van den DRIESSCHE P., Frustration, stability and delay-induced oscillations in a neural network model. SIAM J. of Applied Mathematics, 56, pp. 245-255, 1996.
  • CAMPBELL S.A. & BÉLAIR J., Analytical and symptotically-assisted of Hopf bifurcations in delay-differential equations, Can. Appl. Math. Quart., 3, pp. 137-154, 1995.
  • BÉLAIR J., MACKEY M. & MAHAFFY J., Age-Structured and Two Delay Models for Erythropoiesis, Mathematical Biosciences, 128, pp. 317-346, 1995.
  • MILTON J., CAMPBELL S. & BÉLAIR J., Dynamic feedback and the design of closed-loop drug delivery systems, J. of Biological Systems, 3, pp. 711-718, 1995.
  • CAMPBELL S., BÉLAIR J., OHIRA T. & MILTON J., Limit cycles, tori and complex dynamics in a second-order differential equation with delayed negative feedback, J. of Dynamics and Differential Equations, 7, pp. 213-236, 1995.
  • BÉLAIR J., GLASS L., an der HEIDEN U. & MILTON J., Dynamical Disease : Identification, temporal aspects and treatment strategies of human illness, Chaos, 5, pp. 1-8, 1995.
  • CAMPBELL S., BÉLAIR J., OHIRA T. & MILTON J., Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback, Chaos, 5, pp. 640-645, 1995.
  • CMPBELL, S.A., BÉLAIR J., MILTON J. & OHIRA T., Delayed-displacement-dependent feedback in the dynamics of neuromuscular control : an analytical study, J. Dynamics and Differential Equations, 7, pp. 213-236, 1995.
  • BÉLAIR J. & CAMPBELL S.A., Stability and bifurcations of equilibrio in a multiple-delayed differential equation, SIAM J. Applied Math., 54, pp. 1402-1424, 1994.
  • BÉLAIR J., Stability in a model of a delayed neural network, J. Dynamics Differential Equations, 5, pp 607-623, 1993.
  • BÉLAIR J., Cellules nerveuses, réseaux neuronaux et retards, Morphogenèse et dynamique, ed. D. Barnabé, R. Brunet, Céres, 1, pp. 127-136, 1993.
  • CAMPBELL S.A. & BÉLAIR, J., Delays and tori in a nonlinear model from motor control, Chaos in Biology and Medicine, ed., W. Ditto SPIE 2036, pp. 256-268, 1993.
  • BEUTER A., BÉLAIR J. & LABRIE C., Feedback and Delays in neurological diseases : a modeling study using dynamical systems, Bulletin Math. Biology, 55, pp. 525-541, 1993.
  • BÉLAIR Jacques, Stability in delayed neural networks, Ordinary and delay differential equations, ed. J. Hale, J. Wer & Longnan, 6, pp. 1-4, 1992.
  • BÉLAIR Jacques, Lifespans in populations models : using time delays?, Differential Equation and Applications to Biology and Population Dynamics, ed. S. Busenberg, M. Martelli, Springer, pp. 165-170, 1991.

Actes avec comité de lecture

  • BÉLAIR J. & GLASS L., Introduction to Dynamics in Nonlinear Difference and Differential Equations, in Nonlinear Dynamics in Physiology and Medicine, A. Beuter, L. Glass, M. Mackey & M. Titcombre, eds. Springer, pp. 9-40, 2003.
  • MACKEY M., HAURIE C. & BÉLAIR J., Cell Replication and Control, in Nonlinear Dynamics in Physiology and Medicine, A. Beuter, L. Glass, M. Mackey & M. Titcombre, eds. Springer, pp. 231-268, 2003.
  • BÉLAIR J., Stability in Delayed Neural Networks : Feedback, Circuits and Eigenvalues, in Feedback Circuits and Related Topics, B. Toni, R. Bulajich et P. Pamananda, eds. Facultad de Ciencias UAEM, pp. 14-17, 1999.
  • CAMPBELL S. & BÉLAIR J., Multiple-delayed differential equations as models for biological control systems, in World Congress of Nonlinear Analysis 1992, V. Lakshmikhantham ed. Walter de Gruyter & Co., vol. 4, pp. 3109-3117, 1996.
  • BÉLAIR J. & BEUTER A., Feedback Control of Limb Position : a Random Walk Approach, IEEE Engineering in Medicine and Biology, 17, 1995.
  • BÉLAIR J. & BEUTER A., Feedback and delays in neurological disease : a modeling study using dynamical systems, Brain and Cognition, 28, p. 208, 1995.

Livres

  • BÉLAIR, J., GLASS, L. an der HEIDEN, U. & MILTON, J. (rédacteurs), Dynamical Disease : Mathematical Analysis of Human Illness, 220 pages, American Institute of Physics, New York, 1995.
  • BÉLAIR, J. & DUBUC, S. (rédacteurs), Géométrie fractale et analyse, 472 pages, Kluwer Academic Publishers, Pays-Bas, 1991.

 

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