We consider a wide class of spiking neuron models, defined by rather general set of conditions typical for basic models like leaky integrate and fire, or binding neuron model. A neuron is fed with a point renewal process. A relation between the three probability density functions (pdf): (i) pdf of input interspike intervals, (ii) pdf of output interspike intervals of a neuron with instantaneous...

In this modeling study, we show the combined e ects of gap junctions and GABAergic synapses on the synchronous ring in networks of fast-spiking (FS) interneurons. We found analytically that two identical electrically coupled FS interneurons re synchronously at arbitrary ring frequencies, whereas an FS neuron pair coupled through GABAergic synapses show asynchronous ring. Accordingly, an FS neur...

The basic concepts and techniques involved in the development analysis of mathematical models for individual neurons are reviewed. A spiking neuron model uses differential equations to represent various neuronal activities that have more compatibility with circuit criteria chosen developing a comparative study models. For this comparison, new fully aspects reach balanced is presented. This prov...

A problem of the analysis stochastic effects in multirhythmic nonlinear systems is investigated on basis conceptual neuron map-based model proposed by Rulkov. parameter zone with diverse scenarios coexistence oscillatory regimes, both spiking and bursting, was revealed studied. Noise-induced transitions between basins periodic attractors are analyzed parametrically statistics extracted from num...

Inferior olive (IO) neurons project to the cerebellum and contribute to motor control. They can show intriguing spatio-temporal dynamics with rhythmic and synchronized spiking. IO neurons are connected to their neighbors via gap junctions to form an electrically coupled network, and so it is considered that this coupling contributes to the characteristic dynamics of this nucleus. Here, we demon...

This paper describes the Synapto-dendritic Kernel Adapting Neuron (SKAN), a simple spiking neuron model that performs statistical inference and unsupervised learning of spatiotemporal spike patterns. SKAN is the first proposed neuron model to investigate the effects of dynamic synapto-dendritic kernels and demonstrate their computational power even at the single neuron scale. The rule set defin...

We analyse analytically the coding of information by a spiking neuron. The emphasis is on the question of how many spikes are necessary for the reliable discrimination of two different input signals. The discrimination ability is measured by the second-order Rényi mutual information between the random variable describing the name of the signal and a sequence of n output spikes. Analysing this m...

In this article, we study optimal control problems of spiking neurons whose dynamics are described by a phase model. We design minimum-power current stimuli (controls) that lead to targeted spiking times of neurons, where the cases with unbounded and bounded control amplitude are considered. We show that theoretically the spiking period of a neuron, modeled by phase dynamics, can be arbitrarily...

We demonstrate class I excitability in optically injected microdisk lasers, and propose a possible optical spiking neuron design. The neuron has a clear threshold and an integrating behavior, leading to an output rate-input rate dependency that is comparable to the characteristic of sigmoidal artificial neurons. We also show that the optical phase of the input pulses has influence on the neuron...