Proceedings of 2014 IEEE Workshop on Nonlinear Signal Processing (NSP2014)
Seminar Room, Tokushima University, Tokushima, Japan. December 17 - December 18, 2014

Investigation of Clusteringof Parametrically Excited Oscillatorswith Small Mismatch in Random Network
Kosuke Ooi, Yoko Uwate and Yoshifumi Nishio
Tokushima University
Email: {ooi, uwate, nishio}@ee.tokushima-u.ac.jp
S UMMARY
Synchronization phenomena is one of the fundamental phenomena in nature and it is observed over the various fields. Studies
on synchronization phenomena of coupled oscillators are extensively carried out in various fields, physics [1], biology [2],engineering and so on. It is important to investigate the synchronization phenomena of coupled oscillators for the futureengineering application. The coupled van der Pol oscillator is one of coupled oscillators, and synchronization generated in
the system can model certain synchronization of natural rhythm phenomena. Parametric excitation circuit is one of resonant
circuits, and it is important to investigate various nonlinear phenomena of the parametric excited circuits for future engineering
applications. In simple oscillator including parametric excitation, Ref. [3] reports that the almost periodic oscillation occurs if
nonlinear inductor has saturation characteristic. Additionally the occurrence of chaos is referenced in Refs. [4] and [5].
In our research group, we have investigated synchronization of parametrically excited van der Pol oscillators [6]. By carryingout computer calculations for two or three subcircuits case, we have confirmed that various kinds of synchronization phenomenaof chaos are observed. In the case of two subcircuits, the anti-phase synchronization is observed. In the case of three subcircuits,
self-switching phenomenon of synchronization states is observed.
In our previous study, we investigate synchronization of parametrically excited van der Pol oscillators with small mismatch [7].
The small mismatch is added to the amplitude of the function relating to parametrically excitation. In the case of two subcircuits,
we confirm that the two subcircuits are synchronized at in-phase state when the adding mismatch is small. By increasing thesmall mismatch, we observe unsynchronous phenomena. Furthermore, we applied this circuit model to ten coupled oscillators
as random network model with hub.
In this study, we investigate the clustering of ten coupled oscillators as random network model with hub and without hub
in order to investigate effect of hub for the clustering.
R EFERENCES[1] I. Belykh, M. Hasler, M. Lauret and H. Nijmeijer, “Synchronization and graph topology,” Int. J. Bifurcation and Chaos, vol.15, no.11, pp.3423-3433,
Nov. 2005.
[2] J. Cosp, J. Madrenas, E. Alarcon, E. Vidal and G. Villar, “Synchronization of nonlinear electronic oscillators for neural computation,” IEEE Trans. NeuralNetworks, vol.15, no.5, pp.1315-1327, Sep. 2004.
[3] C. Hayashi, “Nonlinear Oscillations in Physical Systems,” Chap. 11, McGraw-Hill, New York (1964).
[4] C. Hayashi, M. Abe, K. Oshima and H. Kawakami, “The method of mapping as applied to the solution for certain types of nonlinear differential equations,”
Ninth International Conference on Nonlinear Oscillations, Kiev (Aug.-Sep.1981).
[5] M. Inoue, “A Method of Analysis for the Bifurcation of the Almost Periodic Oscillation and the Generation of Chaos in a Parametric Excitation Circuit,”
Trans. of IEICE, vol. J68-A, no. 7, pp. 621-626, 1985.
[6] H. Kumeno, Y. Nishio, “Synchronization Phenomena in Coupled Parametrically Excited van der Pol Oscillators,” Proc. NOLTA’08, pp. 128-131, Sep.
2008.
[7] Kosuke Ooi, Yoko Uwate and Yoshifumi Nishio,“Synchronization and Clustering in Coupled Parametrically Excited Oscillators with Small Mismatch,”
Proc. ISCAS’15 (submitted).

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