The mise en scène of memristive networks: effective memory, dynamics and learning

We discuss the properties of the dynamics of purely memristive circuits. In particular, we show that the amount of memory in a memristive circuit is constrained by the conservation laws of the circuit, and that the dynamics preserves the symmetry by means of a projection on this subspace. We obtain these results both for current and voltage controlled linear memristors. Moreover, we discuss the symmetries of the dynamics which are due to the circuit cohomology, and study the weak and strong non-linear regimes.