Minimum energy spike randomization for neurons

A. Nabi, M. Mirzadeh, F. Gibou, J. Moehlis
2012 2012 American Control Conference (ACC)  
With inspiration from Arthur Winfree's idea of randomizing the phase of an oscillator by driving its state to a set in which the phase is not defined, i.e., the phaseless set, we employ a Hamilton-Jacobi-Bellman approach to design a minimum energy control law that effectively randomizes the next spiking time for a two-dimensional conductance-based model of noisy oscillatory neurons. The control is initially designed for the deterministic system through the numerical solution of the
more » ... of the Hamilton-Jacobi-Bellman partial differential equation for the cost-to-go function, from which the minimum energy stimulus can be found; then its performance is investigated in the presence of noise. It is shown that such control causes a considerable amount of randomization in the timing of the neuron's next spike.
doi:10.1109/acc.2012.6315326 fatcat:3bbfqzlzmrhgvk7luvtlh4gxna