Mathematical Sciences: Mathematical Models for Biological Pattern Formation

本项目将研究胚胎学中模式和形态发育的机制。这是开发和分析数学模型，以产生特定的图案和附属物在被皮上，特别是鳄鱼条纹图案，羽毛和鳞片原始和灵长类动物指纹。这些模型是围绕已知的生物学事实构建的，并将与实验合作者保持密切联系。对构成模型的非线性偏微分方程组进行分析和数值研究。所使用的数学技术将主要是线性分析、非线性分岔理论和数值模拟。发展适当的图形表示的模式解的方程将发挥重要作用。结果和生物学预测将与生物学数据进行比较，并有望用于激励具体的实验，以尝试和阐明真正的模式过程。许多研究与目前正在进行的具体实验研究密切相关。这项工作强调需要将理论研究与实验和观察事实相结合。

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.