相关论文: The Morris-Lecar neuron model embeds a leaky integ…

Morris-Lecar model is arguably the simplest dynamical model that retains both the slow-fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment this model with one slow inward…

Probability density function of output interspike intervals is found in exact form for leaky integrate and fire neuron stimulated with Poisson stream. The diffusion approximation is not exploited.

Leaky-integrate-and-fire (LIF) is studied as a non-linear operator that maps an integrable signal $f$ to a sequence $\eta_f$ of discrete events, the spikes. In the case without any Dirac pulses in the input, it makes no difference whether…

The response of a noisy integrate-and-fire neuron with reset to periodic input is investigated. We numerically obtain the first-passage-time density of the pertaining Ornstein-Uhlenbeck process and show how the power spectral density of the…

Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…

It is well-known that the electrical activities of neurons are induced by a wide variety of external factors. This work considers the effect of electromagnetic induction on improved denatured Morris-Lecar neuron model. The dependence of…

Population equations for infinitely large networks of spiking neurons have a long tradition in theoretical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form…

Spiking neural networks (SNNs) based on Leaky Integrate and Fire (LIF) model have been applied to energy-efficient temporal and spatiotemporal processing tasks. Thanks to the bio-plausible neuronal dynamics and simplicity, LIF-SNN benefits…

The classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic…

Piecewise-deterministic Markov processes combine continuous in time dynamics with jump events, the rates of which generally depend on the continuous variables and thus are not constants. This leads to a problem in a Monte-Carlo simulation…

Spiking Neural Networks (SNNs) have been studied over decades to incorporate their biological plausibility and leverage their promising energy efficiency. Throughout existing SNNs, the leaky integrate-and-fire (LIF) model is commonly…

Spiking neural networks (SNNs) are largely inspired by biology and neuroscience and leverage ideas and theories to create fast and efficient learning systems. Spiking neuron models are adopted as core processing units in neuromorphic…

Leaky integrate-and-fire (LIF) models are mean-field limits, with a large number of neurons, used to describe neural networks. We consider inhomogeneous networks structured by a connec-tivity parameter (strengths of the synaptic weights)…

Spiking Neural Networks (SNNs) use discrete spike sequences to transmit information, which significantly mimics the information transmission of the brain. Although this binarized form of representation dramatically enhances the energy…

We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting…

There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models that describe neuronal activity at the level of the…

We extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find…

Spiking Neural Networks (SNNs) are valued for their ability to process spatio-temporal information efficiently, offering biological plausibility, low energy consumption, and compatibility with neuromorphic hardware. However, the commonly…

Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…

We study a system of perfect integrate-and-fire inhibitory neurons. It is a system of stochastic processes which interact through receiving an instantaneous increase at the moments they reach certain thresholds. In the absence of…