This is a book on mathematical neuroscience, in which the unifying theme is wavelike
phenomena at multiple spatial and temporal scales. There are already several excellent …

The author wishes to describe the development of singular perturbations, including its
history, accumulating literature, and its current status, as he (somewhat personally) …

We describe a robust, adaptive algorithm for the solution of singularly perturbed two-point
boundary value problems. Many different phenomena can arise in such problems, including …

In this chapter, neural field theory is used to model binocular rivalry waves. During binocular
rivalry, visual perception switches back and forth between different images presented to the …

One of the major challenges in neuroscience is to determine how noise that is present at the
molecular and cellular levels affects dynamics and information processing at the …

A stochastic interpretation of spontaneous action potential initiation is developed for the
Morris-Lecar equations. Initiation of a spontaneous action potential can be interpreted as the …

Finding asymptotic solutions to two-point boundary value problems for linear singularly
perturbed second-order ordinary differential equations is now quite well understood …

Following recent advances in imaging techniques and methods of dendritic stimulation,
active voltage spikes have been observed in thin dendritic branches of excitatory pyramidal …

In the small diffusion limit ε→ 0, metastable dynamics is studied for the generalized Burgers
problemformula hereHere u= u (x, t) and f (u) is smooth, convex, and satisfies f (0)= f′(0)= 0 …

We analyze the one-dimensional velocity-jump process, where a particle moves at a
constant velocity determined by the particle's internal velocity state that randomly fluctuates …