Switching synchronization in one-dimensional memristiv networks

Переключення синхронізації у одновимірних мемристорних мережах
Шумовський М. А. (науковий керівник – проф. Першин Ю.В)

Currently, there is strong interest in circuit elements with memory (history-dependent) features. These form a general class of memory circuit elements [1], which includes memory resistors (memristors), memory capacitors (memcapacitors) and memory inductors (meminductors). Quite generally, memristors, memcapacitors and meminductors can be considered as time- and history-dependent generalizations of their standard counterparts. If u(t) and y(t) are any two complementary constitutive circuit variables (current, charge, voltage or flux) denoting the input and the output of the system, respectively, and x is an n-dimensional vector of internal state variables, we may then postulate the existence of the following nth-order u-controlled memory element defined by 

)

,

,

(

)

(

)

(

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,

,

(

)

(

t

u

x

f

t

x

t

u

t

u

x

g

t

y

=

=

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,

(1)
where 
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,

,

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t

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g

is the response function and 
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,

,

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t

u

x

f

is n-component vector function. Currently, the main research effort in the area of memory devices is associated with their non-volatile memory applications [2].

Our interest, however, has been focused on the dynamics of coupled memory circuit elements [3,4]. In fact, networks of memory circuit elements could be used as massively-parallel computing architectures capable to solve certain optimization problems much faster compared to traditional computing hardware. For example, Ref. [3] demonstrates that a network of memristors - a memristive processor - can solve mazes in a massively-parallel way. This approach can be realized experimentally with available systems and devices, or simply implemented on a computer. The hardware implementation of the memristive processor is superior to any existing maze solving methods and therefore it is ideal when the complexity of the maze increases with increasing local connectivity of the graph [3].


In conclusion, we have discovered an interesting synchronization pehnomenon taking place

in one-dimensional memristive networks with elements characterized by a distribution of switching constants. When the switching occurs from the high to low resistance state, the systems with larger switching constants slow down their switching as the voltage falls across these systems decrease faster compared to the voltages across the systems with smaller switching constants. As a re-

sult, the switching of all memristive systems occurs coherently with nearly the same effective rate regardless the specific switching constants of individual systems. This simple picture explains the mechanism of the synchronization effect that is most pronounced when the applied voltage slightly exceeds the combined threshold voltage of memristive systems. We have also demonstrated that

the network switching time is independent on the number of memristive systems (for an appropriately scaled applied voltage) and is defined by the harmonic mean of switching constants.
[1] M. Di Ventra, Y. V. Pershin and L. O. Chua, Circuit elements with memory: memristors, memcapacitors and meminductors  (2009) [Proceedings of the IEEE. 97 (10), 1717-1724]
[2] Y. V. Pershin and M. Di Ventra, Memory effects in complex materials and nanoscale systems (2011) [Advances in Physics. 60 (2), 145-227]
[3] Y. V. Pershin and M. Di Ventra, Solving mazes with memristors: A massively parallel approach (2011) [Physical Review E 84 (4),  046703]
[4] Y. V. Pershin, V. A. Slipko and M. Di Ventra, Complex dynamics and scale invariance of one-dimensional memristive networks  (2013) [Physical Review E 87,  022116]
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