A powerful technique for the analysis of nonlinear oscillators is the rigorous reduction to
phase models, with a single variable describing the phase of the oscillation with respect to …

Many challenging problems that consider the analysis and control of neural brain rhythms
have been motivated by the advent of deep brain stimulation as a therapeutic treatment for a …

High-frequency (HF) deep brain stimulation (DBS) is the gold standard for the treatment of
medically refractory movement disorders like Parkinson's disease, essential tremor, and …

The applicability of phase models is generally limited by the constraint that the dynamics of a
perturbed oscillator must stay near its underlying periodic orbit. Consequently, external …

This is a book about 'Neurodynamics'. What we mean is that this is a book about how ideas
from dynamical systems theory have been developed and employed in recent years to give …

While phase reduction is a tremendously useful tool for understanding the dynamics of
weakly perturbed limit cycle oscillators, its assumptions break down as perturbations …

A procedure is developed for finding an energy-optimal stimulus which gives a positive
Lyapunov exponent, and hence desynchronization, for a neural population. The procedure …

Computationally it was shown that desynchronizing delayed feedback stimulation methods
are effective closed-loop techniques for the control of synchronization in ensembles of …

We develop a novel optimal control algorithm to change the phase of an oscillator using a
minimum energy input, which also minimizes the oscillator's transversal distance to the …

Closed-loop control is a promising deep brain stimulation (DBS) strategy that could be used
to suppress high-amplitude epileptic activity. However, there are currently no analytical …