  We construct an exactly solvable circuit of interacting memristors and study
its dynamics and fixed points. This simple circuit model interpolates between
decoupled circuits of isolated memristors, and memristors in series, for which
exact fixed points can be obtained. We introduce a Lyapunov functional that is
found to be minimized along the non-equilibrium dynamics and which resembles a
long-range Ising Hamiltonian with non-linear self-interactions. We use the
Lyapunov functional as an Hamiltonian to calculate, in the mean field theory
approximation, the average asymptotic behavior of the circuit given a random
initialization, yielding exact predictions for the case of decay to the lower
resistance state, and reasonable predictions for the case of a decay to the
higher resistance state.
