Theoretical Foundations of Memristor Cellular Nonlinear Networks: Stability Analysis With Dynamic Memristors

If the memristor, used in each cell of a memristive variant of the standard space-invariant Cellular Nonlinear Network (CNN), undergoes analogue memductance changes, the processing element operates as a second-order system. The Dynamic Route Map (DRM) technique, applicable to investigate first-order...

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Bibliographic Details
Published inIEEE transactions on circuits and systems. I, Regular papers Vol. 67; no. 4; pp. 1389 - 1401
Main Authors Ascoli, Alon, Messaris, Ioannis, Tetzlaff, Ronald, Chua, Leon O.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.04.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Bistability
Capacitors
Cellular communication
cellular nonlinear networks
Cellular structure
Computer architecture
Dynamic stability
Invariants
memcomputing
Memristor
Memristors
Microprocessors
Nonlinear analysis
Nonlinear dynamical systems
nonlinear dynamics
second-order dynamic route map
Stability analysis
state dynamic portrait
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Summary:If the memristor, used in each cell of a memristive variant of the standard space-invariant Cellular Nonlinear Network (CNN), undergoes analogue memductance changes, the processing element operates as a second-order system. The Dynamic Route Map (DRM) technique, applicable to investigate first-order systems only, is no longer relevant. In this manuscript, a recently introduced methodology, generalizing the DRM technique to second-order systems, is applied to the models of Memristor CNN (M-CNN) cells, accomodating dynamic memristors. This allows to gain insights into the operating principles of these cellular structures, which make computations through the evolution of their states toward prescribed equilibria. Our analysis uncovers all possible local and global phenomena, which may emerge in the cell phase space under zero offset current for any self-feedback synaptic weight. Under these hypotheses, the dynamics of the M-CNN cell may significantly differ from those of a standard space-invariant CNN counterpart. The insertion of an offset current into each cell endows it with further properties, including monostability. The analysis method is used to demonstrate how a non-autonomous memristive array exploits the capability of its cells to feature monostability or bistability, depending upon the respective offset currents, to compute the element-wise logical AND between two binary images.
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2019.2957813