We review the behavior of theoretical models of excitable systems driven by Gaussian white
noise. We focus mainly on those general properties of such systems that are due to noise …

The concepts of equilibrium and nonequilibrium steady states are introduced in the present
review as mathematical concepts associated with stationary Markov processes. For both …

Mixed mode oscillations (MMOs) occur when a dynamical system switches between fast and
slow motion and small and large amplitude. MMOs appear in a variety of systems in nature …

We discuss here the properties of fast global oscillations that emerge in networks of neurons
firing irregularly at a low rate. We first provide a simple introduction to these sparsely …

The activity in the brain cortex remarkably shows a simultaneous presence of robust
collective oscillations and neuronal avalanches, where intermittent bursts of pseudo …

Self-sustained subthreshold oscillations in a discrete-time model of neuronal behavior are
considered. We discuss bifurcation scenarios explaining the birth of these oscillations and …

We demonstrate experimentally that mid-infrared quantum cascade lasers (QCLs) operating
under external optical feedback exhibit extreme pulses. These events can be triggered by …

Mixed-mode oscillations (MMOs) are a complex dynamical behavior in which each cycle of
oscillation consists of one or more large amplitude spikes followed by one or more small …

We study systems which combine both oscillatory and excitable properties, and hence
intrinsically possess two internal frequencies, responsible for standard spiking and for small …

Recent advances in the experimental and theoretical study of dynamics of neuronal
electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal …