The objective of this letter is to convey two essential principles of biological computing—synchronization and memory—in an electronic circuit with two van der Pol (vdP) oscillators coupled via a memristive device. The coupling was mediated by connecting the gate terminals of two programmable unijunction transistors through a resistance-capacitance network comprising an Ag-TiOx-Al memristive device. In the high resistance state the memristance was in the order of MΩ, which leads to two independent self-sustained oscillators characterized by the different frequencies f1 and f2 and no phase relation between the oscillations. Depending on the mediated pulse amplitude, the memristive device switched to the low resistance state after a few cycles and a frequency adaptation and phase locking were observed. The experimental results are underlined by theoretically considering a system of two coupled vdP equations. This experiment may pave the way to larger neuromorphic networks in which the coupling parameters (through memristive devices) can vary in time and strength and are able to remember the history of applied electrical potentials.

1.
S. H.
Strogatz
,
Nature
410
,
268
276
(
2001
).
2.
A.
Pikovsky
,
M.
Rosenblum
, and
J.
Kurths
,
Synchronization: A Universal Concept in Nonlinear Sciences
(
Cambridge University Press
,
Cambridge
,
2001
).
3.
S. H.
Strogatz
,
Phys. D
143
,
1
(
2000
).
4.
A.
Balanov
,
N.
Janson
,
D.
Postnov
, and
O.
Sosnovtseva
,
Synchronization: From Simple to Complex
(
Springer-Verlag
,
City
,
2009
).
5.
A. T.
Winfree
,
The Geometry of Biological Time
(
Springer-Verlag
,
New York
,
1980
).
6.
G. V.
Osipov
,
J.
Kurths
, and
C.
Zhou
,
Synchronization in Oscillatory Networks
, Springer Series in Synergetics (
Springer Verlag
,
New York
,
2007
).
7.
S. H.
Strogatz
,
Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry and Engineering
(
Perseus Books
,
Cambridge, Massachusetts
,
1994
).
8.
P.
Dayan
and
L. F.
Abbott
,
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
(
The MIT Press
,
Cambridge Massachusetts, London
,
2001
).
9.
G.
Shepherd
and
S.
Grillner
,
Handbook of Brain Microcircuits
(
Oxford University Press
,
Oxford
,
2010
).
10.
W.
Gerstner
,
W. H.
Kistler
,
R.
Naud
, and
L.
Paninski
,
Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition
(
Cambridge University Press
,
Cambridge
,
2014
).
11.
E. M.
Izhikevich
,
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting
(
The MIT Press Cambridge
,
Massachusetts London, England
,
2007
).
12.
R. E.
Mirollo
and
S. H.
Strogatz
,
SIAM J. Appl. Math.
50
,
1645
(
1990
).
14.
W.
Singer
and
C. M.
Gray
,
Ann. Rev. Neurosci.
18
,
555
(
1995
).
15.
L. M.
Ward
,
Trends Cognit. Sci.
7
,
553
(
2003
).
16.
F.
Varela
,
J.-P.
Lachaux
,
E.
Rodriguez
, and
J.
Martinerie
,
Nat. Rev. Neurosci.
2
,
229
239
(
2001
).
17.
G.
Buzsaki
,
Rhythms of the Brain
(
Oxford University Press
,
New York
,
2006
).
18.
T.
Aoki
and
T.
Aoyagi
,
Phys. Rev. Lett.
102
,
034101
(
2009
).
19.
M.
Stern
,
H.
Sompolinsky
, and
L. F.
Abott
,
Phys. Rev. E
90
,
062710
(
2014
).
20.
L. O.
Chua
,
IEEE Trans. Circuit Theory
18
,
507
(
1971
).
21.
Memristors and Memristive Systems
, edited by
R.
Tetzlaff
(Springer-Verlag
,
New York
,
2014
).
22.
T.
Ohno
,
T.
Hasegawa
,
T.
Tsurukupka
,
K.
Terabe
,
J. K.
Gimzewski
, and
M.
Aono
,
Nat. Mater.
10
,
591
(
2011
).
23.
Memristor Networks
, edited by
A.
Adamatzky
and
L.
Chua
(
Springer-Verlag
,
New York
,
2014
).
24.
C.
Du
,
W.
Ma
,
T.
Chang
,
P.
Sheridan
, and
W. D.
Lu
,
Adv. Funct. Mater.
25
,
4290
(
2015
).
25.
J. J.
Yang
,
D. B.
Strukov
, and
D. R.
Stewart
,
Nat. Nanotechnol.
8
,
13
24
(
2013
).
26.
M.
Ziegler
,
C.
Riggert
,
M.
Hansen
,
M.
Bartsch
, and
H.
Kohlstedt
,
IEEE TBCAS
9
,
197
(
2015
).
27.
S. H.
Strogatz
and
I.
Stewart
,
Sci. Am.
269
,
102
(
1993
).
28.
B.
van der Pol
,
Philos. Mag.
2
,
978
(
1926
).
29.
B.
van der Pol
,
Philos. Mag.
3
,
65
(
1927
).
30.
B.
van der Pol
and
J.
van der Mark
,
Nature
120
,
363
(
1927
).
31.
N.
Shukla
,
A.
Parihar
,
E.
Freeman
,
H.
Paik
,
G.
Stone
,
V.
Narayanan
,
H.
Wen
,
Z.
Cai
,
V.
Gopalan
,
R.
Engel-Herbert
,
D. G.
Schlom
,
A.
Raychowdhury
, and
S.
Datta
,
Sci. Rep.
4
,
4964
(
2014
).
32.
F. C.
Hoppensteadt
and
E. M.
Izhikevich
,
Biol. Cybern
75
,
117
(
1996
);
[PubMed]
F. C.
Hoppensteadt
and
E. M.
Izhikevich
,
Biol. Cybern
75
,
129
(
1996
).
[PubMed]
33.
34.
Y.
Fang
,
S. P.
Levitan
,
D. M.
Chiarulli
, and
D. H.
Dash
,
Alternative Architecture for Boolean Information Processing Systems in: Emerging Nanoelectronic Devices
(
John Wiley & Sons Ltd
,
2014
), Chap. 24, p.
467
.
35.
F.
Corinto
,
M.
Bonnin
, and
M.
Gilli
,
Int. J. Bifurcation Chaos
17
,
4365
(
2007
).
36.
T. L.
Floyd
,
Electronic Devices
, 5th ed. (
Prentice-Hall-Inc.
,
New Jersey
,
1999
), pp.
608
610
.
38.
D.
Postnov
,
S. K.
Han
, and
H.
Kook
,
Phys. Rev. E
60
,
2799
(
1999
).
39.
R.
Waser
and
M.
Aono
,
Nat. Mater.
6
,
833
(
2007
).
40.
S.
Gaba
,
P.
Sheridan
,
J.
Zhou
,
S.
Choi
, and
W.
Lu
,
Nanoscale
5
,
5872
(
2013
).
You do not currently have access to this content.