Mathematical Sciences: Mathematical Models for Biological Pattern Formation

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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.