Event-based minimum-time control of oscillatory neuron models: phase randomization, maximal spike rate increase, and desynchronization.

We present an event-based feedback control method for randomizing the asymptotic phase of oscillatory neurons. Phase randomization is achieved by driving the neuron's state to its phaseless set, a point at which its phase is undefined and is extremely sensitive to background noise. We consider the biologically relevant case of a fixed magnitude constraint on the stimulus signal, and show how the control objective can be accomplished in minimum time. The control synthesis problem is addressed using the minimum-time-optimal Hamilton-Jacobi-Bellman framework, which is quite general and can be applied to any spiking neuron model in the conductance-based Hodgkin-Huxley formalism. We also use this methodology to compute a feedback control protocol for optimal spike rate increase. This framework provides a straightforward means of visualizing isochrons, without actually calculating them in the traditional way. Finally, we present an extension of the phase randomizing control scheme that is applied at the population level, to a network of globally coupled neurons that are firing in synchrony. The applied control signal desynchronizes the population in a demand-controlled way.