Event-based minimum-time control of oscillatory neuron models

Abstract

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 minimumtime-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.

On a test statistic for the Kuramoto order parameter of synchronization: An illustration for group synchronization during rocking chairs

“…: +1 860 486 3906. nization of firefly flashings [17,18], synchronized applause [19,20], and most recently the Millennium bridge instability [21,22]. Phase synchronization in spike-like oscillatory voltage signals of neural network units has been quantified using the mean voltage signal [23]. Similarly, for chaotic many-body systems the macroscopic oscillation amplitude may be used [24].…”

How to desynchronize quorum-sensing networks

“…Other de-synchronization control methods include e.g. double-pulse stimulation, [31], nonlinear time-delayed feedback [32], phase resetting [33], [34]. Also, in [35], an energyoptimal stimulus was used to control neural spike timing, while in [36], a stimulation-based approach has been developed to control synchrony in neural networks.…”

Neurocontrol: Methods, models and technologies for manipulating dynamics in the brain

“…For example, minimum time control [106], energy-optimal control [107]- [109], and both minimum energy and time control [110]. In [108], a procedure for finding an energyoptimal stimulus was proposed based on computation of Lyapunov exponents.…”