Title: Stable Signal Propagation by Feedforward Networks
Abstract: We survey recent results, obtained jointly with David Wood, on the dynamics of networks in which a (small) network (central pattern generator or CPG) transmits synchronous or phase synchronous signals along one or more feedforward chains. Such propagating signals are common in many areas of biology and are also of interest for continuum robots. Plausible model networks can be constructed as `feedforward lifts’ of the CPG. If the CPG dynamics is periodic, so is the lifted dynamics. Synchrony with the CPG manifests as a standing wave, and a regular phase pattern creates a travelling wave. We discuss the stability (Floquet and Liapunov) of the lifted periodic state to synchrony-breaking perturbations and exhibit stable signals numerically for various standard neuron models.
Joint with David Wood, University of Warwick, UK.
Bio: Ian Stewart is a mathematician who is best-known for engaging the public with mathematics and science through his many bestselling books, newspaper and magazine articles, and radio and television appearances. Ian’s accessible and entertaining style of writing has opened up a range of hard-to-fathom topics — including chaos theory and symmetry — to general audiences.
As an Emeritus Professor at the University of Warwick, Ian splits his time between mathematics research and work to increase awareness of mathematics and science. His research themes cover bifurcation theory, pattern formation and biomathematics, and he has made important contributions to catastrophe theory.
Ian has won a number of prizes for his efforts to further the public’s understanding of science, including the Royal Society’s Michael Faraday Prize in 1995, the 2001 AAAS Public Understanding of Science and Technology Award, the London Mathematical Society’s Zeeman Medal, and Rockefeller University’s Lewis Thomas Prize for writing about science. He has also co-authored four popular science books based on Terry Pratchett’s Discworld novels, as well as himself being a critically acclaimed science fiction author.
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