Locality of interactions for planar memristive circuits

Abstract

Memristors are nonlinear passive circuit elements which can be thought as time varying resistances. When connected in a complex circuit these exhibit very exotic behavior, typical of disordered systems, such as a universal slow relaxation for intricated circuit topologies, and strong dependence on the initial conditions. Being memristive components part of a circuit, non-local effects due to the Kirchhoff constraints are present. In the formalism developed recently for a fairly general class of memristive circuits the constraints are contained in a projection operator. We provide exact results regarding the fall-off of the elements with the Hamming distance on the circuit, thus elucidating an insofar elusive and open question regarding the non-local effects in crossbar arrays, currently being considered for on-chip machine learning.

5.5 pages double column, 4 figures; clarified discussion and corrected typos respect to published version

References in corpus (5)

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• Memristive Networks: from Graph Theory to Statistical Physics
• A mean-field model of memristive circuit interaction
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• Projective Embedding of Dynamical Systems: uniform mean field equations
• Fully analog memristive circuits for optimization tasks: a comparison