相关论文: Parameter Identification Problem in the Hodgkin an…
Multi-compartment Hodgkin-Huxley models are biophysical models of how electrical signals propagate throughout a neuron, and they form the basis of our knowledge of neural computation at the cellular level. However, these models have many…
Mathematical models for the generation of the action potential can improve the understanding of physiological mechanisms that are consequence of the electrical activity in neurons. In such models, some equations involving empirically…
The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables…
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…
The paper addresses the problem of parameter estimation (or identification) in dynamical networks composed of an arbitrary number of FitzHugh-Nagumo neuron models with diffusive couplings between each other. It is assumed that only the…
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,…
To understand the behavior of a neural circuit it is a presupposition that we have a model of the dynamical system describing this circuit. This model is determined by several parameters, including not only the synaptic weights, but also…
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…
Traditionally, parameter estimation in biophysical neuron and neural network models usually adopts a global search algorithm, often combined with a local search method in order to minimize the value of a cost function, which measures the…
How is reliable physiological function maintained in cells despite considerable variability in the values of key parameters of multiple interacting processes that govern that function? Here we use the classic Hodgkin-Huxley formulation of…
The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and…
The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using neurons of the giant squid. It becomes clear that determining experimentally the conductances of neurons…
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…
The classic Hodgkin-Huxley model is widely used for understanding the electrophysiological dynamics of a single neuron. While applying a constant current to the system results in a single voltage spike, it is possible to produce more…
Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters…
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…
In recent years, many difficulties appeared when taking into account the inherent stochastic behavior of neurons and voltage-dependent ion channels in Hodgking-Huxley type models. In particular, an open problem for a stochastic model of…
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomogeneous highly degenerate diffusion for…
We consider a model describing a neuron and the input it receives from its dendritic tree when this input is a random perturbation of a periodic deterministic signal, driven by an Ornstein-Uhlenbeck process. The neuron itself is modeled by…
Single neuron models have a long tradition in computational neuroscience. Detailed biophysical models such as the Hodgkin-Huxley model as well as simplified neuron models such as the class of integrate-and-fire models relate the input…