IEEE Workshop on Nonlinear Signal Processing
December 26, 2016

Spread of Chaotic Behavior
in Coupled Chaotic Circuits with Hub Network
Takahiro Chikazawa, Yoko Uwate, and Yoshifumi Nishio
Dept. of Electrical and Electronic Engineering, Tokushima University,
2-1 Minamijosanjima, Tokushima, 770-8506 Japan
Email: {chikazawa, uwate, nishio}@ee.tokushima-u.ac.jp

Summary
In our society, various type networks which is held on propagation have attracted a great deal of attention from variousfields [1]. These network models have various types of feature quantities. Examples of feature quantities are path length,
degree distribution, and clustering coefficient. Moreover, there are many types of propagation in the real network. For
example, the traffic jam of the transportation network and the pandemic outbreak of of malaria are mentioned. Hence, since
network models become more complex and large scale network, it is more difficult to analyze the phenomena in the networks.
However, there are not many studies of large- scale network of continuous-time real physical systems such as electrical circuits
Therefore, we consider that we can analyze various complicated phenomena of complex networks by investigating the spreadof chaotic behavior.
In our previous studies, we have investigated synchronization phenomena in various types of network [2]. On the otherhand, there is scarcely research results in complex networks. Chaos propagation have been investigated in simple networks
such as a ring combination [3],[4]. In this study, we investigate the spread of chaotic behavior in coupled chaotic circuitswith hub network. We proposed complex network models. These proposed models use chaotic circuits which is called
Nishio-Inaba circuit [5]. One circuit is set to generate chaotic attractor and the other circuits are set to generate three-periodic
attractors. First, we investigate ratio of spreading chaotic behavior in complex network with or without hubs. Moreover, weinvestigate the spread of chaotic behavior in large- scale network with hubs. From the result, we confirm the spread of chaotic
behavior becomes weak in complex network with hub.

References[1] A.L. Barabasi and Z. N. Oltvai, “Network Biology: Understanding the Cell’s Functional Organization,” Nature Reviews
Genetics, Vol. 5, pp.101-113, 2004.
[2] K. Ago, Y. Uwate and Y. Nishio, “Synchronization of Small-World Coupled Chaotic Circuits with or without Parameter
Mismatch,” Proceedings of RISP International Workshop on Nonlinear Circuits, Communications and Signal Processing(NCSP’16), pp. 37-40, Mar. 2016.
[3] Y. Uwate and Y. Nishio, “Chaos Propagation in a Ring of Coupled Circuits Generating Chaotic and Three-Periodic
Attractors,” Proceedings of IEEE Asia Pacific Conference on Circuits and Systems (APCCAS’12), pp. 643-646, Dec.
2012.
[4] T. Chikazawa, S.Tamada, Y. Uwate and Y. Nishio, “Chaos Propagation and Synchronization in Coupled Chaotic Circuitswith Star-and-Ring Combination,” Proceedings of IEEE Workshop on Nonlinear Circuit Networks (NCN’15), pp. 6365, Dec. 2015.
[5] Y. Nishio, N. Inaba, S. Mori and T. Saito, “Rigorous Analyses of Windows in a Symmetric Circuit,” IEEE Transactions
on Circuits and Systems, Vol. 37, no. 4, pp. 473-487, Apr. 1990.

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