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

Francesco Caravelli

Published 2016-11-07Version 1

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, and that the dynamics preserves these symmetry by means of a projection on this subspace. We obtain these results both for current and voltage controlled linear memristors. Moreover, we discuss other symmetries of the dynamics under various transformations, and study the weak and strong non-linear regimes. In the strong regime, we derive a constrained conservation law for the internal memory. In particular, we are able to show that for the case of purely passive or active systems, the eigenvalues of the Jacobian are always real, implying that oscillations can emerge only for mixtures. Our last result concerns the weak non-linear regime, showing that the internal memory dynamics can be interpreted as a constrained gradient descent, and provide the functional being minimized. These results provide another direct connection between memristors and learning.