Spike timing control of oscillatory neuron models using impulsive and quasi-impulsive charge-balanced inputs

Danzl, Per; Moehlis, Jeff

doi:10.1109/acc.2008.4586486

Cited by 20 publications

(13 citation statements)

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“…In addition, controllability of an ensemble of uncoupled neurons was explored for various mathematically ideal phase models, where an effective computational optimal control method based on pseudospectral approximations was employed to construct optimal controls that elicit simultaneous spikes of a neuron ensemble [19,20]. The derivation of time-optimal and spike timing controls for spiking neurons has been attempted for limited classes of control functions [21,22], however, a complete characterization of the optimal solutions has not been provided, and an analytical and systematic approach for synthesizing the time-optimal controls has been missing.…”

Section: Introductionmentioning

confidence: 99%

Design of Charge-Balanced Time-Optimal Stimuli for Spiking Neuron Oscillators

Dasanayake

2014

Neural Computation

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Abstract. In this paper, we investigate the fundamental limits on how the interspike time of a neuron oscillator can be perturbed by the application of a bounded external control input (a current stimulus) with zero net electric charge accumulation. We use phase models to study the dynamics of neurons and derive charge-balanced controls that achieve the minimum and maximum inter-spike times for a given bound on the control amplitude. Our derivation is valid for any arbitrary shape of the phase response curve and for any value of the given control amplitude bound. In addition, we characterize the change in the structures of the charge-balanced time-optimal controls with the allowable control amplitude. We demonstrate the applicability of the derived optimal control laws by applying them to mathematically ideal and experimentally observed neuron phase models, including the widely-studied Hodgkin-Huxley phase model, and by verifying them with the corresponding original full state-space models. This work addresses a fundamental problem in the field of neural control and provides a theoretical investigation to the optimal control of oscillatory systems.

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Section: Introductionmentioning

confidence: 99%

Design of Charge-Balanced Time-Optimal Stimuli for Spiking Neuron Oscillators

Dasanayake

2014

Neural Computation

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“…Therefore, the synchronous properties of (5) depend critically on the nonlinear function PRC s . In this work, as in [13], [14], [16], we assume that the PRC map has particular properties (it is similar to type II PRC from [32]).…”

Section: Phase Synchronizationmentioning

confidence: 99%

“…Phase synchronization is frequently observed in networks of oscillators, like a colony of the smallest free-living eukaryotes [7], the mammalian circadian pacemaker neural network [8], [9] or networks of neural oscillators [10], [3], [11], to mention a few. Controlled phase resetting has been studied in [12], [13], [14], [15] and for a population of oscillators in [16].…”

Section: Introductionmentioning

confidence: 99%

On robustness of phase resetting to cell division under entrainment

Ahmed¹,

Ushirobira²,

Efimov

2015

Journal of Theoretical Biology

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The problem of phase synchronization for a population of genetic oscillators (circadian clocks, synthetic oscillators, etc.) is considered in this paper, taking into account a cell division process and a common entrainment input in the population. The proposed analysis approach is based on the Phase Response Curve (PRC) model of an oscillator (the first order reduced model obtained for the linearized system and inputs with infinitesimal amplitude). The occurrence of cell division introduces state resetting in the model, placing it in the class of hybrid systems. It is shown that without common entraining input in all oscillators, the cell division acts as a disturbance causing phase drift, while the presence of entrainment guarantees boundedness of synchronization phase errors in the population. The performance of the obtained solutions is demonstrated via computer experiments for two different models of circadian/genetic oscillators (Neurospora׳s circadian oscillation model and the repressilator).

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“…The purpose of this paper is to develop elementary control strategies based on this specific tool. An independent but closely related idea has been proposed in [18] in the context of a neuronal model.…”

Section: Introductionmentioning

confidence: 99%