Abstract The Hodgkin and Huxley equations model action potentials in squid giant axons.
Variants of these equations are used in most models for electrial activity of excitable …

In recent years we have seen a tremendous increase in the number of experimentaland
theoretical studies of oscillations and spatialpattern formation in mem-branes. One reason …

We present several topics involving the computation of dynamical systems. The emphasis is
on work in progress and the presentation is informal-there are many technical details which …

We introduce a method for systematically reducing the dimension of biophysically realistic
neuron models with stochastic ion channels exploiting time-scales separation. Based on a …

We have examined the problem of obtaining relationships between the type of stable
solutions of the Hodgkin-Huxley type system, the values of its parameters and a constant …

The model family analyzed in this work stems from the classical Hodgkin-Huxley model
(HHM). for a single-compartment (space-clamp) and continuous variation of the voltage …

We consider the problem of the existence of a negative slope region (NSR) in the voltage-
current curve of the neuronal membrane and the relationship between this phenomenon …

Abstract In Computational Neuroscience, mathematical and computational modeling are
differentiated. In this paper, both kinds of modeling are considered. In particular, modeling …

The rich behavior of neurons—resting states, regular repetitive discharges, patterned
discharges and bursts, and irregular discharges are identified with qualitatively different …

Noticeable in two-parameter bifurcation diagrams for several neural models is the
juxtaposition of cusps and Bogdanov–Takens points. We find parameters for Morris–Lecar …