An electronic device is suggested representing a non-autonomous dynamical system with hyperbolic chaotic attractor of Plykin type in the stroboscopic map, and the results of its simulation with software package NI MULTISIM are considered in comparison with numerical integration of the underlying differential equations. A main practical advantage of electronic devices of this kind is their structural stability that means insensitivity of the chaotic dynamics in respect to variations of functions and parameters of elements constituting the system as well as to interferences and noises.

1.
A. A.
Andronov
,
A. A.
Vitt
, and
S. E.
Khaikin
,
Theory of Oscillators
(
Pergamon
,
Oxford, New York
,
1966
)
2.
L.
Shilnikov
,
Int. J. Bifurcation Chaos
7
,
1353
(
1997
).
3.
M. I.
Rabinovich
and
D. I.
Trubetskov
,
Oscillations and Waves: In Linear and Nonlinear Systems
(Kluwer Academic Dordrecht,
1989
)
4.
S.
Smale
,
Bull. Amer. Math. Soc. (NS)
73
,
747
(
1967
).
5.
R. F.
Williams
,
Publ. Math. de l’I.H.É.S.
43
,
169
(
1974
).
6.
R. V.
Plykin
,
Math. USSR Sb.
23
(
2
),
233
(
1974
).
7.
R. L.
Devaney
,
An Introduction to Chaotic Dynamical Systems
(
Addison-Wesley
,
New York
,
1989
).
8.
J.
Guckenheimer
and
P.
Holmes
,
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
(
Springer
,
New York
,
2002
).
9.
Y. G.
Sinai
, in
Nolinear Waves
edited by
A. V.
Gaponov-Grekhov
(Moscow, Nauka,
1979
) Vol.
192
(in Russian).
10.
A.
Katok
and
B.
Hasselblatt
,
Introduction to the Modern Theory of Dynamical Systems
(
Cambridge University Press
,
Cambridge, New York
,
1995
).
11.
V.
Afraimovich
and
S.-B.
Hsu
,
Lectures on Chaotic Dynamical Systems
, AMS/IP Studies in Advanced Mathematics,
28
, (
American Mathematical Society, Providence, RI; International
,
Somerville, MA
,
2003
).
12.
T. J.
Hunt
and
R. S.
MacKay
,
Nonlinearity
16
,
1499
(
2003
).
13.
C. A.
Morales
,
Ann. Inst. Henri Poincaré
13
,
589
(
1996
), http://www.numdam.org/item?id=AIHPC_1996__13_5_589_0.
14.
V.
Belykh
,
I.
Belykh
, and
E.
Mosekilde
,
Int. J. Bifurcation Chaos
15
,
356
(
2005
).
15.
T. J.
Hunt
,
Low dimensional dynamics: Bifurcations of cantori and realisations of uniform hyperbolicity
,” Ph.D. thesis (
University of Cambridge
,
2000
).
16.
J. S.
Aidarova
and
S. P.
Kuznetsov
,
Izvestija VUZov – Prikladnaja Nelineinaja Dinamika
16
(
3
),
176
(
2008
) [English translation: http://xxx.lanl.gov/abs/0901.2727].
17.
S. P.
Kuznetsov
,
Phys. Rev. Lett.
95
,
144101
(
2005
).
18.
S. P.
Kuznetsov
and
E. P.
Seleznev
,
JETP
102
,
355
(
2006
).
19.
S. P.
Kuznetsov
and
A.
Pikovsky
,
Physica D
232
,
87
(
2007
).
20.
O. B.
Isaeva
,
S. P.
Kuznetsov
, and
E.
Mosekilde
,
Phys. Rev. E
84
,
016228
(
2011
).
21.
S. P.
Kuznetsov
,
JETP
106
,
380
(
2008
).
22.
S. P.
Kuznetsov
,
Phys. Usp.
54
(
2
),
119
(
2011
).
23.
See http://www.ni.com/multisim/ for NI MULTISIM.
24.
S. P.
Kuznetsov
,
Commun. Nonlinear Sci. Numer. Simul.
14
,
3487
(
2009
).
25.
S. P.
Kuznetsov
,
Chaos
19
,
013114
(
2009
).
26.
S. P.
Kuznetsov
,
Nonlinear Dyn.
5
,
403
(
2009
) (in Russian), http://nd.ics.org.ru/doc/r/pdf/1551/0.
27.
P.
Horowitz
and
W.
Hill
,
The Art of Electronics
, 2nd ed. (
Cambridge University Press
,
Cambridge
,
1989
).
28.
L. O.
Chua
,
Scholarpedia J.
2
(
10
),
1488
(
2007
).
29.
P. D.
Hiscocks
,
Analog Circuit Design
(
Syscomp Electronic Design Ltd.
,
2005–2010
), http://syscompdesign.com/AnalogBook.html.
30.
Y.-C.
Lai
,
C.
Grebogi
,
J. A.
Yorke
, and
I.
Kan
,
Nonlinearity
6
,
779
(
1993
).
31.
V. S.
Anishchenko
,
A. S.
Kopeikin
,
J.
Kurths
,
T. E.
Vadivasova
, and
G. I.
Strelkova
.
Phys. Lett. A
270
,
301
(
2000
).
32.
P. V.
Kuptsov
and
S. P.
Kuznetsov
,
Phys. Rev. E
80
,
016205
(
2009
).
33.
G.
Benettin
,
L.
Galgani
,
A.
Giorgilli
, and
J.-M.
Strelcyn
,
Meccanica
15
,
9
(
1980
).
34.
J. L.
Kaplan
and
J. A.
Yorke
, in
Functional Differential Equations and Approximations of Fixed Points. Lecture Notes in Mathematics
, edited by
H.-O.
Peitgen
and
H.-O.
Walther
(
Springer
,
Berlin, N.Y
,
1979
), Vol.
730
, p.
204
.
35.
T.
Yang
,
Int. J. Comput. Cognit.
2
(
2
),
81
(
2004
), http://www.yangsky.us/ijcc/pdf/ijcc11a.pdf
36.
A. S.
Dmitriev
and
A. I.
Panas
,
Dynamical Chaos: New Information Carriers for Communication Systems
(Moscow, Fizmatlit,
2002
) (in Russian).
37.
A. A.
Koronovskii
,
O. I.
Moskalenko
, and
A. E.
Hramov
,
Phys.Usp.
52
,
1213
(
2009
).
38.
39.
M. S.
Baptista
,
Phys. Lett. A
240
,
50
(
1998
).
40.
J. M.
Amigó
,
Intelligent Computing Based on Chaos (Studies in Computational Intelligence)
, (
Springer-Verlag
,
Berlin, Heidelberg
,
2009
) Vol.
184
, p.
291
.
41.
J. M.
Carroll
,
J.
Verhagen
, and
P. T.
Wong
,
Cryptologia
16
(
1
),
52
(
1992
).
42.
T.
Stojanovski
and
L.
Kocarev
,
IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
48
(
3
),
281
(
2001
).
43.
T.
Stojanovski
,
J.
Pihl
, and
L.
Kocarev
,
IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
48
(
3
),
382
(
2001
).
44.
The accuracy the curves are depicted grows fast with increase of N. Actually, N = 6 is enough to get so small errors that they are visually indistinguishable in the plot.
You do not currently have access to this content.