"The Control of Frequency of a Conditional Oscillator..."
MAR 30, 2012 | 4:00 PM TO 6:00 PM
The Graduate Center
365 Fifth Avenue
March 30, 2012: 4:00 PM-6:00 PM
Initiative for the Theoretical Sciences (ITS) sponsored Applied Mathematics Seminar
Conditional Oscillator Simultaneously Subjected to Multiple Oscillatory Inputs
The gastric mill network of the crab Cancer borealis is an oscillatory network with frequency ~ 0.1 Hz. Oscillations in this network require neuromodulatory synaptic inputs as well as rhythmic inputs from the faster (~ 1 Hz) pyloric neural oscillator. We study how the frequency of the gastric mill network is determined when it receives rhythmic input from two different sources but where the timing of these inputs may differ. We find that over a certain range of the time difference one of the two rhythmic inputs plays no role what so ever in determining the network frequency while in another range, both inputs work together to determine the frequency. The existence and stability of periodic solutions to model sets of equations are obtained analytically using geometric singular perturbation theory. The results are validated through numerical simulations. Comparisons to experiments are also presented.