Phase Change of Three Coupled Chaotic Circuits toInput Signals
Takahiro Hattori, Yoko Uwate and Yoshifumi Nishio
Dept. of Electrical and Electronic Engineering
Tokushima University
2-1 Minami-Josanjima, Tokushima 7708506, Japan
E-mail: {hattori, uwate, nishio}@ee.tokushima-u.ac.jp

resistor as a current . In this study, we investigate thesynchronization phenomenon when the amplitude of thesinusoidal input signal is varied using the circuit experiment.
The amplitude of the sinusoidal input signal is.

Abstract— In this study, the synchronization state of a threephase coupled chaotic circuit with an external sinusoidal input
signal is investigated by circuit experiments. As a result, it isconfirmed that the synchronization state changes when theamplitude of the sinusoidal input signal is varied.
Keywords; Synchronization; Chaotic circuit;I.

INTRODUCTION

Synchronization phenomena can be found in various
aspects of daily life. A typical example is the oscillation of ametronome. Research on engineering applications of chaos has
also attracted the attention of many researchers. Encoding andcompounding of communications, synchronization phenomena
in neurons of the human brain, etc. is observed and areexpected to be applied to computers in the brain. Furthermore,
the observation and analysis of phenomena using electric
circuits is one of the most useful tools because it can be applied
to actual physical systems. Therefore, it is very important tostudy synchronous phenomena in chaotic circuits for futureengineering applications. In a previous study, synchronization
phenomena were investigated when input signals are added totwo chaotic circuits coupled by resistors [1]-[4].

(a) Chaotic circuit.

In this study, a coupled three-phase chaos circuit is createdby coupling three chaos circuits, and synchronization
phenomena are investigated when an external sinusoidal signal
is added to the circuit system. Specifically, a sinusoidal signal
with the amplitude and frequency of the current of a chaoticcircuit is used as the standard input signal. The synchronization
phenomenon is investigated when the amplitude of thissinusoidal input signal is varied. Current waveforms areobtained from circuit experiments.

II.

(b) Coupled three chaotic circuits with input signal.
Figure 1. System Model.

SYSTEM MODEL

The chaotic circuit used in this study is shown in Fig.1(a).
The circuit in Fig.1(a) is a 3-D autonomous circuit thatgenerates the chaos shown in Fig.2 and proposed by Inaba andMori [5]. This circuit consists of a negative resistor, twoinductors, a capacitor, and a diode. In the circuit shown inFig.1(b), the three Inaba circuits are coupled by a single
coupling resistor R. The input signal is added to the coupling978-1-6654-5971-6/22/$31.00 ©2022 IEEEFigure 2. An example of chaotic attractors.

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III.

C. In the case of about doubled amplitude of the standard
input signal
Figure 5 shows the result of doubled amplitudes. It is foundthat under the influence of the input signal, the two chaotic
circuits are nearly synchronized, while one chaotic circuit andthe sinusoidal signal are nearly antiphase synchronized.

RESULTS

Figures 3, 4, and 5 show the results using circuit
experiments. A sinusoidal signal with the amplitude andfrequency of the current of the chaotic circuit is used as thestandard value. The amplitude of the current in that sinusoidal
signal is set to 2.5 [mA]. The amplitude is varied by a factor of0, 1, and 2 to investigate how the phase changes.

I[25mA/div]
A. In the case of no input signal
Figure 3 shows the result of no input signal. It is found thethree chaos circuits are almost synchronized in three phases.
I[25mA/div]→time[0.2ms/div]
Figure 5. In the case of about doubled amplitude of the standard input signal→time[0.2ms/div]

current characteristics.

=100mH,=10mH, C=33nF and R=110Ω.

Figure 3. In the case of no input signal current characteristics.
=100mH,=10mH, C=33nF and R=110Ω.

IV.
B. In the case of the standard input signal
Figure 4 shows the result of the standard input signal. It isfound that the three chaotic circuits and the sinusoidal signal
are synchronized in almost four phases under the influence ofthe input signal.
I[25mA/div]

CONCLUSIONSIn this study, we investigated the synchronization state of acoupled three-phase chaotic circuit with input signals using
circuit experiments. The synchronization state changes with thevalue of the amplitude of the input signal, a sinusoidal signal. It
is found a new synchronization phenomenon, especially when
the amplitude is doubled. As a future work, we would like toinvestigate the case when the value of angular frequency isvaried and when the input signal is a square wave signal.
Ⅴ. REFERENCES
[1]

[2]

[3]

[4]

→time[0.2ms/div]
Figure 4. In the case of the standard input signal current characteristics.
=100mH,[5]=10mH, C=33nF and R=110Ω.

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