The effect of noise on the Chaffee-Infante Equation: a nonlinear case study

We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, ut - [Delta]u = [beta]u - u3, by noise. While a single multiplicative Itô noise of sufficient intensity will stabilise the origin, its Stratonovich counterpart leaves the dimension of the attractor essentially unchanged. We then show that a collection of multiplicative Stratonovich terms can make the origin exponentially stable, while an additive noise of sufficient richness reduces the random attractor to a single point