  The process of pattern formation for a multi-species model anchored on a time
varying network is studied. A non homogeneous perturbation superposed to an
homogeneous stable fixed point can amplify, as follows a novel mechanism of
instability, reminiscent of the Turing type, instigated by the network
dynamics. By properly tuning the frequency of the imposed network evolution,
one can make the examined system behave as its averaged counterpart, over a
finite time window. This is the key observation to derive a closed analytical
prediction for the onset of the instability in the time dependent framework.
Continuously and piecewise constant periodic time varying networks will be
analysed, to set the ground for the proposed approach. The extension to non
periodic settings will also be discussed.
