Asymptotic and Singular Perturbation Methods for Bifurcation Problems with Applications

研究人员和他的同事们研究了激光稳定性问题和生化振荡器领域中出现的一系列新的数学问题。激光问题是由激光动力学变量的不同时间尺度引起的奇异摄动问题，或出现在半导体激光器的延迟-微分方程组的研究中。所有这些问题都是由合作完成的实验引起的。生物化学振子问题也是描述有丝分裂等级联酶反应模型中出现的奇异摄动问题。研究活动的一个重要部分集中在激光不稳定性上。激光用于许多应用(通讯、外科手术)，也是我们日常生活的一部分(激光打印机、超市的条形码读取、CD机)。但这些激光器通常是不稳定的设备。分析激光器响应的数学困难阻碍了对它们的控制。这位研究人员和他的同事提议使用更先进的数学技术来解决这些问题。

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.