Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:A4L-C

Session:

Number:162

Investigation of Synchronizations in Five Cross-Coupled Chaotic Circuits

Naoto Kageyama,  Yoko Uwate,  Yoshifumi Nishio,  

pp.162-165

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.162

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Summary:
Studies on chaos synchronization in coupled chaotic circuits are extensively carried out in various fields. In this study, we investigate synchronization phenomena observed in five simple chaotic circuits cross-coupled by five inductors. Interesting synchronization phenomena can be confirmed by computer simulations.

References:

[1] Ch. von der Malsbuurg and J. Buhmann, “Sensory Segmentation with Coupled Neural Oscillators,” Biol. Cybern., vol. 67, pp. 233-242, 1992.

[2] N. Platt, E.A. Spiegel and C. Tresser, “On-Off Intermittency: A Mechanism for Bursting,” Phys. Rev. Lett., vol. 70, no. 3, pp. 279-282, 1993.

[3] P. Ashwin, J. Buescu and I. Stewart, “Bubbling of Attractors and Synchronization of Chaotic Oscillators,” Phys. Lett. A,193, pp. 126-139, 1994.

[4] E. Ott and J.C. Sommerer, “Blowout Bifurcations: the Occurrence of Riddled Basins and On-Off Intermittency,” Phys. Lett. A,199, pp. 39-47, 1994.

[5] Y. Nishio and A. Ushida, “Spatio-Temporal Chaos in Simple Coupled Chaotic Circuits,” IEEE Trans. Circuits Syst. I, vol. 42, no. 10, pp. 678-686, 1995.

[6] N.F. Rulkov and M.M. Sushchik, “Robustness of Synchronized Chaotic Oscillations,” Int. J. Bifurcation and Chaos, vol. 7, no. 3, pp. 625-643, 1997.

[7] M. Wada, Y. Nishio and A. Ushida, “Analysis of Bifurcation Phenomena in Two Chaotic Circuits Coupled by an Inductor,” IEICE Trans. Fundamentals, vol. E80-A, no. 5, pp. 869-875, 1997.

[8] Y. Nishio and A. Ushida, “Chaotic Wandering and its Analysis in Simple Coupled Chaotic Circuits,” IEICE Trans. Fundamentals, vol. E85-A, no. 1, pp. 248-255, 2002.

[9] G. Abramson,V.M. Kenkre and A.R. Bishop, “Analytic Solutions for Nonlinear Waves in Coupled Reacting Systems,” Physica A: Statistical Mecanics and its Applications, vol. 305, no. 3-4, pp. 427-436, 2002.

[10] 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, 2005.

[11] Y. Uchitani and Y. Nishio, “Investigation of State Transition Phenomena in Cross-Coupled Chaotic Circuits,” Proc. of ISCAS'08, pp. 2394-2397, May 2008.

[12] Y. Uchitani and Y. Nishio, “Synchronization Patterns Generated in a Ring of Cross-Coupled Chaotic Circuits,” Proc of IJCNN'08, pp. 3854-3859, Jun. 2008.

[13] Y. Uchitani and Y. Nishio, “Synchronization of Small Oscillations in Cross-Coupled Chaotic Circuits,” Proc of ISCAS'09, pp. 2629-2632, May 2009.

[14] N. Kageyama, Y. Uwate and Y. Nishio, “Detailed Investigation of Synchronizations in Three Cross-Coupled Chaotic Circuits,” Proc. of NCSP'13, pp. 628-631, Mar. 2013.

[15] M. Shinriki, M. Yamamoto and S. Mori, “Multi-Mode Oscillations in a Modified van der Pol Oscillator Containing a Positive Nonlinear Conductance,” Proc. of IEEE, vol. 69, pp. 394-395, 1981.