平成 27 年度電気関係学会四国支部連合大会 講演論文集 (2015 高知工科大学)
2015 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (KOCHI)

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Investigation of Oscillation Frequencies
of Coupled Chaotic Circuits
Misa SEKIMOTO

Yoko UWATE
Yoshifumi NISHIO(Tokushima University)

1. Introduction

0.48 to make it easier to compare transition of oscillation
frequency.

Synchronous discrimination of the chaotic circuit uses
the phase diﬀerence generally. Not only the phase difference but also period and oscillation frequency exist in
the coupled chaotic circuits. We pay attention to oscillation frequency in the coupled chaotic circuits. We consider
that entire circuits synchronize when oscillation frequency
included in a certain circuit converges on a certain value.
In this study, we compare synchronous discrimination byusing phase diﬀerence and oscillation frequency.
As simulation result, we confirm that synchronous stateof chaotic circuits has no relationship with the oscillation
frequency, although oscillation frequency converges on asteady value conclusively. Next, we compare timing ofsynchronization of among the coupled chaotic circuits. We
investigate whether there is relationship in the timing ofsynchronization as we determine synchronous state of circuit by using oscillation frequency or phase diﬀerence.

3. Simulation results
Figure 2 shows transition of oscillation frequency when
the coupling strength is changed.

2. Circuit model

Figure 2: Transition of oscillation frequency when theWe use chaotic circuits called Nishio-Inaba circuit [1].
We consider a ladder network using chaotic circuits asshown in Fig. 1.

value of α are set equability(α2 = 0.41, α3 = 0.435, α4 =0.46).
We set parameters α2 = 0.41, α3 = 0.435, α4 = 0.46.
From Fig. 2, n(a − b) is indicated circuit state between
circuit number a and b. In addition, we surround thecoupling strength with circle when the phase diﬀerence isbelow 30 degrees. Each circuit does not synchronize whenoscillation frequency converges on a steady value. And,oscillation frequencies are obtained a stable value before
entire circuit becomes synchronization.
Next, we pay attention to timing of synchronization ofamong the coupled chaotic circuits. Timing of synchronization are investigated using oscillation frequency andthe phase diﬀerence. As a result, timing of synchronization between oscillation frequency and phase diﬀerence has
no relationship.

Figure 1: Setting condition of parameter αn ( n = 5,α2 =α3 =α4 =the variable ).
Normalized equation of coupled chaotic circuits is described as follow,

x˙n = αxn + zn .
y˙n = zn − f (yn ).
z˙n = −xn − βyn + σ(z( n + 1) − zn ),4. Conclusions(n = 1)In this study, we investigated oscillation frequencies of
two coupled chaotic circuits. We confirmed that frequency
became closer to a value when synchronization state waschanged from asynchronous into synchronous, and there isno similarity in each timing. From these, we confirm thatsynchronous state of chaotic circuits has no relationshipwith the oscillation frequency.

z˙n = −xn − βyn + σ(z( n − 1) − zn ),(n = the maximum value)z˙n = −xn − βyn + σ(z( n + 1) + z( n − 1) − 2zn ),(otherwise)(1)
For this simulation, the parameters are set as follows,
βn = 3.0 and γn = 470.0. Own oscillation frequency andphase diﬀerence of the chaotic circuits depend on the parameter α. Each circuit is assigned α to investigate transition of oscillation frequency when the chaotic circuits aresynchronized. Parameter α is fixed value 0.40 ≤ α ≤ 0.48.
In addition, the parameter α1 and αn located in both endsof coupled chaotic circuit are fixed α1 = 0.40 and αn =References[1] Y. Nishio, N. Inaba, S. Mori and T. Saito, “Rigorousanalyses of windows in a symmetric circuit,” IEEE
Trans. Circuits Syst., Vol. 37, No. 4, pp. 473-487,
1990.

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