Turing’s Work in Bifurcation Theory and Pattern Formation

演讲人: Alan Garfinkel 加州大学洛杉矶分校
时间: 2013-10-17 14:00-2013-10-17 15:00

 In 1952, Alan Turing published a paper of great importance, “The Chemical Basis of Morphogenesis”. The paper introduced a radical new paradigm for the explanation of the emergence of patterns: a homogeneous system of chemicals, reacting with each other, and diffusing through a spatial medium, can spontaneously develop structures. The key to this emergence is the presence of symmetry-breaking bifurcations in a set of Partial Differential Equations. 

I will review the history of this work and its progress in the 60 years since its publication, and argue that it represents a major conceptual revolution in biology, that is only now reaching its height.  Examples will be given from physiology and pathophysiology, including the development of branching structures in the lung and of pathological lesions in atherosclerosis.


 Alan Garfinkel is Professor of Medicine at UCLA, working in the area of mathematical modeling in physiology. He earned degrees in Philosophy and Mathematics from Cornell and Harvard Universities. He began his career as a Philosophy Professor, but then changed fields and joined the UCLA Department of Medicine, where he specializes in the mathematics of cardiac arrhythmias and the mathematical modeling of pattern formation.