TOPICS IN MATHEMATICAL BIOLOGY

数学生物学主题

• 批准号: 5211983
• 负责人: RONALD E MICKENS
• 金额: --
• 依托单位国家: 美国
• 资助国家: 美国
• 起止时间: 至
• 项目状态: 未结题
• 来源: https://reporter.nih.gov/project-details/5211983
• 关键词: DNA; biological models; chemical structure; ecology; heart; kidney; mathematical model; mathematics; model design /development; nucleic acid structure; physiology

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.

我们的研究工作将集中在使用各种数学方法 复差分与复差分解析法 在生物学、生态学和生物科学的系统建模中出现的方程 生理学。感兴趣的特定系统包括： *周期性疾病 *肾脏浓缩机制 *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 *药物分配(区隔模式) 得到精确解、近似解和数值解。这个 要使用的数学方法包括摄动(规则和 奇异)和渐近级数，调和平衡程序，相空间 分析、混沌系统的“理论”和数值积分。