Mathematics Colloquia and Seminars

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In the Crayfish swimmeret system, each segment contains a half-center oscillator responsible for controlling the power stroke and return stroke motoneurons.  The half-center oscillator is made up of two strongly connected neurons, each with their own phase response properties.  Each segment is capable of oscillations independent of other segments, however all segments are connected to each other by weak intersegmental coupling.  Because of this, we may use the theory of weakly coupled oscillators in an effort to deduce how phase maintenance is achieved in the cord over varying frequencies.  First, we need the phase response properties of the individual segments.  We analyze the half-center oscillator in one module, and through an idealized phase model derive the infinitesimal phase response curve (iPRC) of the half-center oscillator (HCO) from the iPRC of the individual cells.  The phase locking properties of a chain of HCO are studied for various parameters.  The work is then compared to experimental data from the Crayfish swimmeret system.