相关论文: Quantized Single-Ion-Channel Hodgkin-Huxley Model …
Synchronization in neural networks is strongly tied to the implementation of cognitive processes, but abnormal neuronal synchronization has been linked to a number of brain disorders such as epilepsy and schizophrenia. Here we examine the…
The Hodgkin-Huxley (HH) model is the currently accepted formalism of neuronal excitability. However, the HH model does not capture a number of biophysical behaviors associated with action potentials or propagating nerve impulses. Physical…
The opening or closing mechanism of a voltage-gated ion channel is triggered by the potential difference crossing the cell membrane in the nervous system. Based on this picture, we model the ion channel as a nanoscale two-terminal ionic…
The influence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic…
Memristors are resistive elements retaining information of their past dynamics. They have garnered substantial interest due to their potential for representing a paradigm change in electronics, information processing and unconventional…
A spiking neuron ``computes'' by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a…
This article develops a fundamental insight into the behavior of neuronal membranes, focusing on their responses to stimuli measured with power spectra in the frequency domain. It explores the use of linear and nonlinear (quadratic…
In this work we are interested in a mathematical model of the collective behavior of a fully connected network of finitely many neurons, when their number and when time go to infinity. We assume that every neuron follows a stochastic…
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…
In this work the stochastic generalization of single Hodgkin-Huxley neuron is further extended to unidirectionally coupled neurons. Our main focus is to elucidate the role of channel noise in the kinetics and energetics of spiking of action…
This article is devoted to the theoretical and numerical analysis of a network of excitatory and inhibitory neurons of Hodgkin-Huxley (HH) type, for which the topology is inspired by that of a single local layer of visual cortex V1. Our…
Influence of mesoscopic channel noise on excitable dynamics of living cells became a hot subject within the last decade, and the traditional biophysical models of neuronal dynamics such as Hodgkin-Huxley model have been generalized to…
By means of the concepts of factorial moment, return map and NM estimator, we analyze some responses of a HH neuron to various types of spike-train inputs. The corresponding fractal dimensions and values of NM estimators can describe the…
In a succession of articles published over 65 years ago, Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical understanding of excitation in nerve, and how the axon conducts the action potential.…
Using a stochastic generalization of the Hodgkin–Huxley model, we consider the influence of intrinsic channel noise on the synchronization between the spiking activity of the excitable membrane and an externally applied periodic…
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…
The Hodgkin-Huxley model of nerve pulse propagation relies on ion currents through specific resistors called ion channels. We discuss a number of classical thermodynamic findings on nerves that are not contained in this classical theory.…
The activation of a $K^+$ channel sensor in two sequential stages during a voltage clamp may be described as the translocation of a Brownian particle in an energy landscape with two large barriers between states. A solution of the…
This work explores four nonlinear classical models of neural oscillators, the Hodgkin-Huxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Nonlinear contraction theory is used to develop observers…
The Hodgkin-Huxley model describes action potential generation in certain types of neurons and is a standard model for conductance-based, excitable cells. Following the early work of Winfree and Best, this paper explores the response of a…