The memristor is a device whose resistance changes depending on the polarity
and magnitude of a voltage applied to the device's terminals. We design a
minimalistic model of a regular network of memristors using
structurally-dynamic cellular automata. Each cell gets info about states of its
closest neighbours via incoming links. A link can be one 'conductive' or
'non-conductive' states. States of every link are updated depending on states
of cells the link connects. Every cell of a memristive automaton takes three
states: resting, excited (analog of positive polarity) and refractory (analog
of negative polarity). A cell updates its state depending on states of its
closest neighbours which are connected to the cell via 'conductive' links. We
study behaviour of memristive automata in response to point-wise and spatially
extended perturbations, structure of localised excitations coupled with
topological defects, interfacial mobile excitations and growth of information
pathways.Comment: Accepted to Int J Bifurcation and Chaos (2011
