Duality rules in circuits containing memristors and other nonlinear elements (Keynote)

Duality rules in circuits containing memristors and other nonlinear elements (Keynote)

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The classical duality principle, introduced by Russel in 1904, is limited to circuits built from R-C-L elements. This concept was extended by Itoh and Chua in 2013 to memristors, memcapacitors, and meminductors. It will be shown in this talk that these two concepts of the duality are special subsets of a more general principle, which has interesting associations with Chua’s table (CT) of fundamental circuit elements and with the equivalent storeyed structure (SS). It turns out that the combination of associated flip-type, shift-type, and translational-type transformations of the circuit elements in the CT or SS can generate dual networks with interesting features. It is demonstrated on nonlinear dynamic systems and processes how such regularities of the duality can be used for their modeling, hardware emulation, or synthesis. As a particular consequence of these transformations, systems built from memristors can be adequately studied via their dual “easy-to-built” circuits which exhibit exactly the same behavior, but now observable in different coordinates. It can be used for constructing effective hardware emulators of bioinspired systems containing memristors.

The classical duality principle, introduced by Russel in 1904, is limited to circuits built from R-C-L elements. This concept was extended by Itoh and Chua in 2013 to memristors, memcapacitors, and meminductors. It will be shown in this talk that these two concepts of the duality are special subsets of a more general principle, which has interesting associations with Chua’s table (CT) of fundamental circuit elements and with the equivalent storeyed structure (SS). It turns out that the combination of associated flip-type, shift-type, and translational-type transformations of the circuit elements in the CT or SS can generate dual networks with interesting features. It is demonstrated on nonlinear dynamic systems and processes how such regularities of the duality can be used for their modeling, hardware emulation, or synthesis. As a particular consequence of these transformations, systems built from memristors can be adequately studied via their dual “easy-to-built” circuits which exhibit exactly the same behavior, but now observable in different coordinates. It can be used for constructing effective hardware emulators of bioinspired systems containing memristors.

memristor; higher-order element

memristor; higher-order element

BIOLEK, D.

2020

08.07.2019

TU Dresden

Dresden, Germany

20

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