Mathematical Sciences: Mathematical Models for Biological Pattern Formation

本项目将研究参与的机制 胚胎学中的模式和形式的发展。 这是为了 开发和分析数学模型， 特别是鳄鱼皮上的花纹和附属物 条纹图案、羽毛和鳞片原基以及灵长类 指纹 这些模型是围绕已知的生物 事实和密切联系将保持与实验 合作者 非线性偏微分方程组， 构成模型将进行分析研究， 数字上的 使用的数学技术主要是 线性分析、非线性分叉理论和数值计算 仿真 编制适当的图表， 方程的模式解将在 部分 结果和生物学预测将进行比较 与生物学数据相结合，并有望用于激励 尝试和阐明真实的模式的特殊实验 过程 许多研究都与特定的 目前正在进行实验研究。 工作强调， 需要将理论研究与实验和 观察事实

This project will study the mechanisms involved in the development of pattern and form in embryology. This is to develop and analyze mathematical models for generating specific patterns and appendages on the integument, specifically alligator stripe patterns, feather and scale primordia and primate fingerprints. The models are constructed around known biological facts and close contact will be maintained with experimental collaborators. The nonlinear partial differential equation systems which constitute the models will be investigated analytically and numerically. The mathematical techniques used will primarily be linear analysis, nonlinear bifurcation theory and numerical simulation. Development of appropriate graphical presentation of the patterned solutions of the equations will play an important part. The results and biological predictions will be compared with the biological data and hopefully will be used to motivate specific experiments to try and elucidate the real patterning process. Much of the research is closely linked to specific experimental studies currently underway. The work emphasizes the need for integrating theoretical studies with experimental and observational facts.