How Do Cockroaches Run So Fast Without Thinking About It?

Philip Holmes, Apr. 21, 2008

I will discuss joint work with John Schmitt, Raffaele Ghigliazza, Justin Seipel, Raghavendra Kukillaya, Bob Full and Dan Koditschek, in which nonlinear mechanics and hybrid dynamical systems meet biology. Motivated by Full's experimental studies of running insects at UC Berkeley, we propose a hierarchy of models for the dynamics of legged locomotion. We start with energetically conservative bipedal models (each leg corresponding to the front/rear/opposite-middle stance tripod used by many insect species), move on to activated hexapedal models, and end by describing a central pattern generator of bursting neurons linked via simplified muscles to more realistic leg geometries. I believe that massive, detail-packed simulations do not necessarily confer understanding, and in reviewing our work, I shall stress the relevance of simple models.

The talk uses linear algebra and differential equations, introduces necessary background from biomechanics and neuroscience.

Philip Holmes was born in North Lincolnshire, UK, in 1945 and studied engineering at the Universities of Oxford and Southampton, where he fell among mathematicians and began working on nonlinear dynamics and chaos. In 1977 he emigrated to the US. He taught at Cornell University until 1994, when he moved to Princeton, where he is now Professor of Mechanics and Applied Mathematics. Most of his current work is in biology and neuroscience, addressing the question "How are neural spikes turned into behavior?" Collaborating with biologists, neuroscientists and psychologists, he approaches this through studies of running cockroaches, swimming lampreys, and thinking humans. He has co-authored over 200 papers and four books, including "Celestial Encounters" with Florin Diacu: an historical account of the origins of chaos theory. He is a Fellow of the American Academy of Arts and Sciences and a Foreign Member of the Hungarian Academy of Sciences. He has also published four collections of poems; the most recent, "Lighting the Steps," appeared from Anvil Press (London, UK) in 2002.