TOPICS IN MATHEMATICAL BIOLOGY

我们的研究工作将集中在使用各种数学 复数差分和微分的求解与分析技巧 在生物学、生态学和生物学系统建模中出现的方程， physiology. 感兴趣的特定系统包括： * 周期性疾病 * 肾浓缩机制 * 生化振荡器 * 反应-平流过程 * 人口的长期波动 * DNA分子的非线性模型 * 药物分布（房室模型） 将获得精确、近似和数值解。 的 所使用的数学技术包括扰动（常规的和 奇异）和渐近级数，谐波平衡法，相空间 分析，混沌系统的“理论”和数值积分。

Our research efforts will center on the use of a variety of mathematical techniques to solve and analyze the complex difference and differential equations that arise in the modeling of systems in biology, ecology and physiology. Particular systems of interest include: * periodic diseases * the renal concentrating mechanism * biochemical oscillators * reaction-advection processes * long-term fluctuations of populations * nonlinear models of the DNA molecule * drug distribution (compartmental models) Exact, approximate and numerical solutions will be obtained. The mathematical techniques to be used include perturbation (both regular and singular) and asymptotic series, harmonic balance procedures, phase-space analysis, the 'theory' of chaotic systems, and numerical integration.