Related papers: Multiscale modeling via split-step methods in neur…
Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new…
We demonstrate that our recently developed theory of electric field wave propagation in anisotropic and inhomogeneous brain tissues, which has been shown to explain a broad range of observed coherent synchronous brain electrical processes,…
We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system…
In this paper we construct a mathematical model for excitable membranes by introducing circuit characteristics for ion pump, ion current activation, and voltage-gating. The model is capable of reestablishing the Nernst resting potentials,…
The generation of action potential brings into play specific mechanosensory stimuli manifest in the variation of membrane capacitance, resulting from the selective membrane permeability to ions exchanges and testifying to the central role…
Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and close states of ion channels. Although it has previously been shown that channel noise can nontrivially…
Neural encoding is a field in neuroscience that focuses on characterizing how information from stimuli is encoded in the spiking activity of neurons. When more than one stimulus is present, a theory known as multiplexing posits that neurons…
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…
This paper presents a rigorous mathematical analysis, alongside simulation studies, of a spatially extended stochastic electrophysiology model, the Hodgkin-Huxley model of the squid giant axon being a classical example. Although most…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
Neurons are the central biological objects in understanding how the brain works. The famous Hodgkin-Huxley model, which describes how action potentials of a neuron are initiated and propagated, consists of four coupled nonlinear…
Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane but also contribute to an additional charging of the cell membrane resulting in the…
In this paper we deal with a feedback control design for the action potential of a neuronal membrane in relation with the non-linear dynamics of the Hodgkin-Huxley mathematical model. More exactly, by using an external current as a control…
We analyze the effects of noise on the traveling wave dynamics in neural fields. The noise influences the dynamics on two scales: first, it causes fluctuations in the wave profile, and second, it causes a random shift in the phase of the…
Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often, these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
The effect of intrinsic channel noise is investigated for the dynamic response of a neuronal cell with a delayed feedback loop. The loop is based on the so-called autapse phenomenon in which dendrites establish not only connections to…
Neurons in the brain continuously process the barrage of sensory inputs they receive from the environment. A wide array of experimental work has shown that the collective activity of neural populations encodes and processes this constant…