2006 IEEE Workshop on Nonlinear Circuit Networks (NCN'06)
Tokushima University, Tokushima, Japan, Dec. 9, 2006

Investigation of Asymmetrical Coupled
Chaotic Circuit Systems
Yasuteru Hosokawa

Yoshifumi Nishio

Dept. Information Science,
Shikoku University
Email: hosokawa@keiei.shikoku-u.ac.jp

Dept. Electrical and Electronics,
Tokushima University
Email: nishio@ee.tokushima-u.ac.jp

Abstract— In this study, some kinds of asymmetrical asymmetrical coupled chaotic circuit systems are investigated. Systems
consist of two kinds of chaotic circuits. Each circuits are coupled
globally. In these system, an interesting phenomena including
synchronization phenomena are observed. The phenomenon isthat a ratio of the synchronization time increases in spite ofincreasing parameter mismatches in the system.

subcircuit A and B ). Figure 2 shows one of the computer sim-I. I NTRODUCTION
Coupled chaotic systems generate various kinds of complex higher-dimensional phenomena such as spatio-temporalchaotic phenomena, clustering phenomena and so on. Oneof the most studied systems may be the coupled map latticeproposed by Kaneko[1]. The advantage of the coupled map
lattice is its simplicity. However, many of nonlinear phenomena generated in nature would be not so simple. Therefore, it
is important to investigate the complex phenomena observedin natural physical systems such as electric circuits systems
In this study, some kinds of asymmetrical global coupledchaotic systems are investigated. Especially, we pay attention to relationships between synchronization phenomena andsmall parameter mismatches. In these systems, an interesting
phenomenon is observed. The phenomenon is that a ratio of thesynchronization time increases in spite of increasing parametermismatches in the system.
II. S YSTEM M ODEL
G

subcircuitAG

subcircuit
AGGGG

GG

subcircuit
Bsubcircuit
BFig. 2.
Relationship of the ratio of the synchronization time and small
parameter mismatches. m = 2, n = 3, pk = 0.001(k − 1), α = 0.400,
β = 0.500, γ = 20.0 and δ = 0.070

ulation results. In this case, Shinriki’s circuit[2] is applied assubcircuits. The asymmetry is realized by using two coupling
point. Horizontal axis shows small parameter mismatches (Q)and vertical axis shows the ratio of the synchronization time.
The ratio of the synchronization time of A-subcircuit is increased by increasing small parameter mismatches. Normally,
the ratio of the synchronization time is decreased by increasing
small parameter mismatches. However, this phenomena show
the opposite result. We suppose that the phenomenon can beexplained as follows. The synchronizations of the one subcircuit group and the other subcircuit group are constricted eachother. Therefore, in the case of decreasing the synchronizationof one group, the synchronization of the other group increases.
Same phenomena are observed other systems.
III. C ONCLUSIONSGG

In this study, we reported about an investigation of asymmetrical coupled chaotic circuit systems.

subcircuit
BR EFERENCES
Fig. 1.

System Model

Figure 1 shows a system model in this study. This system
consists of two kinds of subcircuits and resistors as couplingelements. Subcircuits are coupled globally. An asymmetry of
the system is realized by using two kinds of subcircuits ([1] K. Kaneko, “Clustering, Coding, Switching, Hierarchical Ordering, andControl in a Network of Chaotic Elements,” Physica D, vol. 41, pp. 137–172, 1990.
[2] M. Shinriki, M. Yamamoto and S. Mori, “Multimode Oscillations in
a Modified van der Pol Oscillator Containing a Positive Nonlinear
Conductance,” Proc. IEEE, vol. 69, pp. 394–395, 1981.

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