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Linear synchronization and circuit implementation of chaotic system with complete amplitude control *

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Chunbiao Li at Nanjing University of Information Science and Technology
Chunbiao Li
Wesley Joo-Chen Thio
Wesley Joo-Chen Thio
Wesley Joo-Chen Thio
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Julien Clinton Sprott at University of Wisconsin–Madison
Julien Clinton Sprott
Ruo-Xun若洵 Zhang张
Ruo-Xun若洵 Zhang张
Ruo-Xun若洵 Zhang张
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Abstract

Although chaotic signals are considered to have great potential applications in radar and communication engineering, their broadband spectrum makes it difficult to design an applicable amplifier or an attenuator for amplitude conditioning. Moreover, the transformation between a unipolar signal and a bipolar signal is often required. In this paper, a more intelligent hardware implementation based on field programmable analog array (FPAA) is constructed for chaotic systems with complete amplitude control. Firstly, two chaotic systems with complete amplitude control are introduced, one of which has the property of offset boosting with total amplitude control, while the other has offset boosting and a parameter for partial control. Both cases can achieve complete amplitude control including amplitude rescaling and offset boosting. Secondly, linear synchronization is established based on the special structure of chaotic system. Finally, experimental circuits are constructed on an FPAA where the predicted amplitude control is realized through only two independent configurable analog module (CAM) gain values.
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Chin. Phys. B Vol. 26, No. 12 (2017) 120501
Linear synchronization and circuit implementation of chaotic system
with complete amplitude control∗
Chun-Biao Li(李春彪)1,2,†, Wesley Joo-Chen Thio3, Julien Clinton Sprott4,
Ruo-Xun Zhang(张若洵)5, and Tian-Ai Lu(陆天爱)1,2
1Jiangsu Key Laboratory of Meteorological Observation and Information Processing,
Nanjing University of Information Science & Technology, Nanjing 210044, China
2School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China
3Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA
4Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA
5College of Teacher Education, Xingtai University, Xingtai 054001, China
(Received 11 July 2017; revised manuscript received 22 August 2017; published online 20 October 2017)
Although chaotic signals are considered to have great potential applications in radar and communication engineering,
their broadband spectrum makes it difficult to design an applicable amplifier or an attenuator for amplitude conditioning.
Moreover, the transformation between a unipolar signal and a bipolar signal is often required. In this paper, a more intelli-
gent hardware implementation based on field programmable analog array (FPAA) is constructed for chaotic systems with
complete amplitude control. Firstly, two chaotic systems with complete amplitude control are introduced, one of which has
the property of offset boosting with total amplitude control, while the other has offset boosting and a parameter for partial
control. Both cases can achieve complete amplitude control including amplitude rescaling and offset boosting. Secondly,
linear synchronization is established based on the special structure of chaotic system. Finally, experimental circuits are con-
structed on an FPAA where the predicted amplitude control is realized through only two independent configurable analog
module (CAM) gain values.
Keywords: complete amplitude control, amplitude rescaling, offset boosting, linear synchronization
PACS: 05.45.–a, 05.45.Ac, 05.45.Xt DOI: 10.1088/1674-1056/26/12/120501
1. Introduction
Chaotic signals have great potential applications in radar
and communication engineering because of their broadband
frequency spectrum.[1–20]However, this introduces a corre-
sponding challenge to signal-conditioning since it is difficult
to construct an amplifier or a polarity conversion circuit with
a broadband frequency response. The chaotic signal usually
cannot meet the amplitude requirement for practical applica-
tions. Polarity conversion is also critical since some integrated
circuits require either unipolar or bipolar signals. Although
some effort has been made to realize amplitude control for
chaotic signal through total amplitude scaling and partial am-
plitude scaling,[21–24]the polarity control of chaotic signal has
not received the same attention despite being essential in elec-
tronic engineering.[25–28]
Offset boosting is associated with the DC component of
the variable, and our study shows that one or more variables
in a chaotic system can obtain offset boosting by introduc-
ing a new constant.[26]Consequently the conversion between
a unipolar chaotic signal and a bipolar signal can be realized
by a single DC source or a control rheostat rather than a com-
plicated hardware peripheral unit. Foregoing research has al-
lowed us to realize a system with complete amplitude control
by using amplitude scaling and offset boosting. As shown in
Fig. 1, the signal modulator is replaced by two controllers for
amplitude rescaling and offset boosting, giving complete con-
trol of the chaotic signals for chaos application systems.
chaotic
system
(CS)
amplitude
rescaling
(AR)
ARC
OBC
complete
controlled
chaotic
signal
chaos
based
application
system
(CAS)
signal
modulator
(SM)
signal
control unit
(SCU)
offset
boosting
(OB)
Fig. 1. Application system with chaos.
In this paper, a whole linear control of chaotic signals is
explored through amplitude and offset control in a single sys-
tem, and a linear synchronization between two systems is de-
scribed. We consider two cases of complete amplitude control
∗Project supported by the Startup Foundation for Introducing Talent of Nanjing University of Information Science & Technology, China (Grant No. 2016205),
the Natural Science Foundation of the Jiangsu Higher Education Institutions of Jiangsu Province, China (Grant No. 16KJB120004), the Priority Academic
Program Development of Jiangsu Higher Education Institutions, and the Natural Science Foundation of Hebei Province, China (Grant No. A2015108010).
†Corresponding author. E-mail: goontry@126.com; chunbiaolee@nuist.edu.cn
© 2017 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb　　　http://cpb.iphy.ac.cn
120501-1
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