Asymptotic and Singular Perturbation Methods for Bifurcation Problems with Applications

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Erneux9973203 The investigator and his colleagues study a series of newmathematical problems appearing in the area of laser stabilityproblems and in the area of biochemical oscillators. The laserproblems are singular perturbation problems that result from thedifferent time scales of the laser dynamical variables or thatappear in the study of delay-differential equations modelingsemiconductor lasers. All these problems are motivated byexperiments that are done in collaboration. The biochemicaloscillator problems are also singular perturbation problems thatappear in models of cascading enzyme reactions describing, forexample, mitosis. An important part of the research activities concentrates onlaser instabilities. Lasers are used in many applications(communication, surgery) and are part of our every-day life(laser printers, bar code reading at the supermarket, CDplayers). But these lasers are often unstable devices.Mathematical difficulties in analyzing the responses of theselasers have prevented their control. The investigator and hiscolleagues propose to use more advanced mathematical techniquesin order to solve these problems.