In this paper, an experimental characterization of the dynamical properties of five autonomous chaotic oscillators, based on bipolar-junction transistors and obtained de-novo through a genetic algorithm in a previous study, is presented. In these circuits, a variable resistor connected in series to the DC voltage source acts as control parameter, for a range of which the largest Lyapunov exponent, correlation dimension, approximate entropy, and amplitude variance asymmetry are calculated, alongside bifurcation diagrams and spectrograms. Numerical simulations are compared to experimental measurements. The oscillators can generate a considerable variety of regular and chaotic sine-like and spike-like signals.
References
1.
K.
Aihara
, G.
Matsumoto
, and Y.
Ikegaya
, J. Theor. Biol.
109
, 249
(1984
).2.
H.
Korn
and P.
Faure
, C. R. Biol.
326
, 787
(2003
).3.
Y.
Hirata
, M.
Oku
, and K.
Aihara
, Chaos
22
, 047511
(2012
).4.
S. R. Dtchetgnia
Djeundam
, R.
Yamapi
, T. C.
Kofane
, and M. A.
Aziz-Alaoui
, Chaos
23
, 033125
(2013
).5.
K.
Aihara
and G.
Matsumoto
, J. Theor. Biol.
95
, 697
(1982
).6.
H.
Hayashi
and S.
Ishizuka
, J. Theor. Biol.
156
, 269
(1992
).7.
H.
Gu
, Chaos
23
, 023126
(2013
).8.
C. J.
Stam
, Clin. Neurophys.
116
, 2266
(2005
).9.
W. J.
Freeman
, Neurodynamics: An Exploration in Mesoscopic Brain Dynamics, Perspectives in Neural Coding
(Springer
, 2000
).10.
V. N.
Belykh
, G. V.
Osipov
, V. S.
Petrov
, J. A. K.
Suykens
, and J.
Vandewalle
, Chaos
18
, 037106
(2008
).11.
L. V.
Gambuzza
, A.
Cardillo
, A.
Fiasconaro
, L.
Fortuna
, J.
Gómez-Gardeñes
, and M.
Frasca
, Chaos
23
, 043103
(2013
).12.
L.
Fortuna
and M.
Frasca
, Chaos
17
, 043118
(2007
).13.
I.
Pehlivan
, Y.
Uyaroğlu
, and O.
Önal
, in Proceedings of the 6th International Advanced Technologies Symposium, Elazığ, Turkey, 16–18 May 2011
(2011
), p. 360
.14.
G. M.
Bernstein
and M. A.
Lieberman
, MILCOM'89
3
, 640
(1989
).15.
R. M.
Nguimdo
, R.
Tchitnga
, and P.
Woafo
, Chaos
23
, 043122
(2013
).16.
H.
Nomura
, N.
Wakami
, and S.
Kondo
, Proc. IEEE Int. Conf. Fuzzy Syst.
5
, 57
(1995
).17.
L.
Minati
, in Proceedings of the 8th International Symposium on Image and Signal Processing and Analysis, ISPA, Trieste, Italy
(2013
), p. 748
.18.
19.
A. S.
Elwakil
and M. P.
Kennedy
, IEEE Trans. Circuits Syst.
47
, 582
(2000
).20.
A. S.
Elwakil
and M. P.
Kennedy
, Microelectron. J.
31
, 459
(2000
).21.
J. X.
Li
, Y. Cai
Wang
, and F. C.
Ma
, Nonlinear Dyn.
72
, 575
(2013
).22.
E.
Lindberg
, K.
Murali
, and A.
Tamasevicius
, IEEE Trans. Circuits Syst.
52
, 661
(2005
).23.
F.
Takens
, Dynamical Systems and Bifurcations
, Lecture Notes in Mathematics (Springer
, New York
, 1985
), Vol. 1125, pp. 99
–106
.24.
R.
Tchitnga
, H. B.
Fotsin
, B.
Nana
, P. H. Louodop
Fotso
, and P.
Woafo
, Chaos, Solitons Fractals
45
, 306
(2012
).25.
M. P.
Hanias
, I. L.
Giannis
, and G. S.
Tombras
, Chaos
20
, 013105
(2010
).26.
E.
Ott
, Chaos in Dynamical Systems
(Cambridge University Press
, Cambridge
, 2002
).27.
E.
Lindberg
, Nonlinear Dyn.
44
, 219
(2006
).28.
H.
Kantz
and T.
Schreiber
, Nonlinear Time Series Analysis
(Cambridge University Press
, Cambridge
, 1997
).29.
R.
Hegger
, B.
Kantz
, and T.
Schreiber
, Chaos
9
, 413
(1999
).30.
M.
Fraser
and H. L.
Swinney
, Phys. Rev. A
33
, 1134
(1986
).31.
M. B.
Kennel
, R.
Brown
, and H. D. I.
Abarbanel
, Phys. Rev. A
45
, 3403
(1992
).32.
J.
Theiler
, J. Opt. Soc. Am. A
7
, 1055
(1990
).33.
A.
Provenzale
, L. A.
Smith
, R.
Vio
, and G.
Murante
, Physica D
58
, 31
(1992
).34.
H.
Kantz
, Phys. Lett. A
185
, 77
(1994
).35.
H.
Kantz
, T.
Schreiber
, I.
Hoffmann
, T.
Buzug
, G.
Pfister
, L. G.
Flepp
, J.
Simonet
, R.
Badii
, and E.
Brun
, Phys. Rev. E
48
, 1529
(1993
).36.
T.
Sauer
and J.
Yorke
, Int. J. Bifurcation Chaos
3
, 737
(1993
).37.
S.
Pincus
, Chaos
5
, 110
(1995
).38.
See http://www.mathworks.it/matlabcentral/fileexchange/32427-fast-approximate-entropy for the source code.
39.
B.
Davis
, J.
Jovicich
, V.
Iacovella
, and U.
Hasson
, Cereb. Cortex
24
, 1332
(2014
).40.
J.
Kengne
, J. C.
Chedjou
, V. A.
Fono
, and K.
Kyamakya
, Nonlinear Dyn.
67
, 1247
(2012
).41.
E.
Lindberg
, K.
Murali
, and A.
Tamacevicius
, in Proceedings of the 14th International Workshop on Nonlinear Dynamics Electronic Systems, NDES2006, Dijon, France
(2006
), p. 108
.42.
O.
Tsakiridis
, D.
Syvridis
, E.
Zervas
, and J.
Stonham
, in 3rd WSEAS International Conference on Electronics Hardware Wireless Optical Communication, WSEAS2004, Salzburg, Austria
(2004
), p. 482
.43.
C. C.
Canavier
, J. W.
Clark
, and J. H.
Byrne
, Biophys. J.
57
, 1245
(1990
).44.
M. J.
Ogorzalek
, Z.
Galias
, A. M.
Dabrowski
, and W. R.
Dabrowski
, IEEE Trans. Circuit Sys.
42
, 706
(1995
).45.
M.
Cencini
, M.
Falcioni
, E.
Olbrich
, H.
Kantz
, and A.
Vulpiani
, Phys. Rev. E
62
, 427
(2000
).46.
P.
Grassberger
and I.
Procaccia
, Physica D
9
, 189
(1983
).47.
J. S.
Richman
and J. R.
Moorman
, Am. J. Physiol.: Heart Circ. Physiol.
278
, 2039
(2000
).48.
D. J.
Daley
and D.
Vere-Jones
, An Introduction to the Theory of Point Processes
(Springer
, New York
, 1988
).49.
T.
Sauer
, Phys. Rev. Lett.
72
, 3811
(1994
).50.
See supplementary material at http://dx.doi.org/10.1063/1.4890530 for additional waveforms, spectra and netlists.
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