It is generally believed that students learn best through activities that require their direct participation. By using simulations as a tool for learning neuroscience, students are directly engaged in the activity and obtain immediate feedback and reinforcement. This paper describes a series of biophysical models and computer simulations that can be used by educators and students to explore a v...

The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may p...

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capabl...

We present a physiologically plausible binaural mechanism for the perception of the pitch of complex sounds via ghost stochastic resonance. In this scheme, two neurons are driven by noise and a different periodic signal each (with frequencies f(1)=kf(0) and f(2)=(k+1)f(0), where k>1), and their outputs (plus noise) are applied synaptically to a third neuron. Our numerical results, using the Mor...

This article concerns the phenomenon of Mixed-Mode Bursting Oscillations (MMBOs). These are solutions of fast-slow systems of ordinary differential equations that exhibit both small-amplitude oscillations (SAOs) and bursts consisting of one or multiple large-amplitude oscillations (LAOs). The name MMBO is given in analogy to Mixed-Mode Oscillations, which consist of alternating SAOs and LAOs, w...

Low frequency firing is modeled by Type 1 neurons with a SNIC, but, because of the vertical slope of the square-root-like f-I curve, low f only occurs over a narrow range of I. When an adaptive current is added, however, the f-I curve is linearized, and low f occurs robustly over a large I range. Ermentrout (Neural Comput. 10(7):1721-1729, 1998) showed that this feature of adaptation paradoxica...

We consider a stochastic version of an excitable system based on the Morris-Lecar model of a neuron, in which the noise originates from stochastic sodium and potassium ion channels opening and closing. One can analyze neural excitability in the deterministic model by using a separation of time scales involving a fast voltage variable and a slow recovery variable, which represents the fraction o...

Dendritic and axonal processes of nerve cells, along with the soma itself, have membranes with spatially distributed densities of ionic channels of various kinds. These ionic channels play a major role in characterizing the types of excitable responses expected of the cell type. These densities are usually represented as constant parameters in neural models because of the difficulty in experime...

We present a physiologically plausible binaural mechanism for the perception of the pitch of complex sounds via ghost stochastic resonance. In this scheme, two neurons are driven by noise and a different periodic signal each (with frequencies f1 = kf0 and f2 = (k+1)f0, where k > 1), and their outputs (plus noise) are applied synaptically to a third neuron. Our numerical results, using the Morri...