  Biological neuronal networks are characterized by nonlinear interactions and
complex connectivity. Given the growing impetus to build neuromorphic
computers, understanding physical devices that exhibit structures and
functionalities similar to biological neural networks is an important step
toward this goal. Self-organizing circuits of nanodevices are at the forefront
of the research in neuromorphic computing, as their behavior mimics synaptic
plasticity features of biological neuronal circuits. However, an effective
theory to describe their behavior is lacking. This study provides for the first
time an effective mean field theory for the emergent voltage-induced
polymorphism of \textit{circuits} of a nanowire connectome, showing that the
behavior of these circuits can be explained by a low-dimensional dynamical
equation. The equation can be derived from the microscopic dynamics of a single
memristive junction in analytical form. We test our effective model on
experiments of nanowire networks and show that it fits both the potentiation
and depression of these synapse-mimicking circuits. We show that our theory
applies beyond the case of nanowire networks by formulating a general
mean-field theory of conductance transitions in self-organizing memristive
connectomes.
