  In a common experimental setting, the behaviour of a noisy dynamical system
is monitored in response to manipulations of one or more control parameters.
Here, we introduce a structured model to describe parametric changes in
qualitative system behaviour via stochastic bifurcation analysis. In
particular, we describe an extension of Gaussian Process models of transition
maps, in which the learned map is directly parametrized by its fixed points and
associated local linearisations. We show that the system recovers the behaviour
of a well-studied one dimensional system from little data, then learn the
behaviour of a more realistic two dimensional process of mutually inhibiting
neural populations.
