Saddle-Node Bifurcations in Brain Dynamics
Mathematical methods have important applications in the neurosciences. This talk investigates some of these. A network operating in a state x*(t) has interesting dynamics if it is near a bifurcation; that is, near where changes in the stability of x*(t), such as the onset of oscillations, can result from small changes in the network. Saddle-Node bifurcations are particularly interesting since they are in some senses the most likely to occur, but they are difficult to study since they typically involve knowing global behavior of solutions. They arise in studies of signal processing of neural signals. This talk will: derive a cononical model near a multiple saddle-node bifurcation in a general network, lift the canonical model to an oscillatory network, which is based on Voltage Controllled Oscillator Nueron models(VCONs), use VCONs to model the action potential trigger region of a neuron, analyze signal processing aspects of VCON networks, describe wave propagation in VCON networks, and discuss aspects of these networks related to brain science.
Refreshments at 3:30pm in Math 401N.