We investigate the stability of traveling-pulse solutions to the stochastic FitzHugh–Nagumo
equations with additive noise. Special attention is given to the effect of small noise on the …

Bistability is a key property of many systems arising in the nonlinear sciences. For example,
it appears in many partial differential equations (PDEs). For scalar bistable reaction …

We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus,
driven by space-time white noise, and with a time-periodic drift term, which vanishes on two …

In this work, we study early-warning signs for stochastic partial differential equations
(SPDEs), where the linearization around a steady state has continuous spectrum. The …

We analyze the effect of additive fractional noise with Hurst parameter H> 1/2 H> 1/2 on fast-
slow systems. Our strategy is based on sample paths estimates, similar to the approach by …

The main objective of this thesis is to analyse the dynamical behaviour of different linear and
non-linear stochastic heat equations using analytical and probabilistic techniques. We begin …