The study of stochastic dynamics and bifurcation analysis in oscillatory systems has emerged as a pivotal field in understanding how random perturbations interact with nonlinear processes. At its core ...

We use asymptotic methods to analyze the effects of discreteness and random noise on a mathematical model of the lithiation/delithiation dynamics of a single electrode nanoparticle. We begin by ...

The previous framework (left) fails to take into account noises of the brain. The brain state transitions were written as point-to-point, the dynamics as deterministic, and the control cost as the ...