Abstract
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 neighbors via incoming links. A link can be "conductive" or "nonconductive". States of every link are updated depending on the states of cells the link connects. Every cell of a memristive automaton assumes 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 neighbors which are connected to the cell via "conductive" links. We study behavior of memristive automata in response to point-wise and spatially extended perturbations, structure of localized excitations coupled with topological defects, interfacial mobile excitations and growth of information pathways.
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