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.
We designed a minimalistic model of a two-dimensional discrete memristive medium. Every site of such medium takes triple states, and a binary conductivity of links is updated depending on states of sites the links connect. The model is a hybrid between classical excitable cellular automata and classical structurally-dynamic cellular automata. A memristive automaton with binary cell-states would give us even more elegant model however by using binary cell-states we could not easily detect source and sink of simulated 'currents'. Excitable cellular automata provide us with all necessary tools to imitate current polarity and to control local conductivity. From topology of excitation wave-fronts and wave-fragments we can even reconstruct relative location of a source of initiated current.
We defi ned two type of memristive cellular automata and characterised their space-time dynamics in response to point-wise and spatially extended perturbations. We classi ed several regimes of automata excitation activity, and provided detailed accounts of most common types of oscillating localizations. We did not undertake any systematic search for minimal oscillators though but just exempli ed two most commonly found after random spatially-extended stimulation. Exhaustive search for all possible localised oscillations could be a topic of further studies.
With regards to formation of conductive pathways just few possible versions amongst many implementable were discussed in the papers. Opportunities to grow 'wires' in memristive automata are virtually unlimited.
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