The tools of weakly coupled phase oscillator theory have had a profound impact on the
neuroscience community, providing insight into a variety of network behaviours ranging from …

This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and
the dynamical influence of correlation time and noise intensity in a bistable Duffing–Van der …

We develop a perturbation method for studying quasineutral competition in a broad class of
stochastic competition models and apply it to the analysis of fixation of competing strains in …

We demonstrate an analytical method for calculating the phase sensitivity of a class of
oscillators whose phase does not affect the time evolution of the other dynamic variables …

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we
establish a method to derive a hybrid system approximating the noise-induced coherent …

The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle
oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators …

Patterns of spatial synchrony of population dynamics are dramatic phenomena that provide
the potential for unraveling forces controlling the dynamics of natural populations in time and …

We formulate a theory for the collective phase description of globally coupled noisy limit-
cycle oscillators exhibiting macroscopic rhythms. Collective phase equations describing …

We study the effect of additive Brownian noise on an ODE system that has a stable
hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is …

Objective. Almost 30 years after the start of the modern era of deep brain stimulation (DBS),
the subthalamic nucleus (STN) still constitutes a standard stimulation target for advanced …