  Our main interest in this paper is the study of homogenised limit of a
parabolic equation with a nonlinear dynamic boundary condition of the
micro-scale model set on a domain with periodically place particles. We focus
on the case of particles (or holes) of critical diameter with respect to the
period of the structure. Our main result proves the weak convergence of the
sequence of solutions of the original problem to the solution of a
reaction-diffusion parabolic problem containing a `strange term'. The novelty
of our result is that this term is a nonlocal memory solving an ODE. We prove
that the resulting system satisfies a comparison principle.
