Switching Synchronization Phenomena ofa Ring of Coupled Chaotic Circuitswith One-Direction Time-Delayed Effects
Seiya Kita

Yoko Uwate

Yoshifumi Nishio

Dept. of Elec. and Elec. Eng.,
Tokushima University
kita@ee.tokushima-u.ac.jp

Dept. of Elec. and Elec. Eng.,
Tokushima University
uwate@ee.tokushima-u.ac.jp

Dept. of Elec. and Elec. Eng.,
Tokushima University
nishio@ee.tokushima-u.ac.jp

S UMMARY
Studies on synchronization state are extensively carried out in various fields [1]-[3]. Recently, in particular, the synchronization
states in chaotic oscillators are studied by many researchers. The behavior of chaotic oscillators is interesting. Then, the chaos
phenomena are quite dependent on initial values and not periodical and predictable. Moreover the synchronization states havecaused very interesting phenomena. A synchronization and the related the bifurcation of chaotic systems are good methods todescribe various high-dimensional nonlinear phenomena in the field of natural science. However, many synchronization statesof coupled chaotic oscillators have not been solved yet. The synchronization phenomena in the electric circuit make clear
the mechanism of the synchronization phenomena in our daily life. There are many nonlinear systems containing time delay,
such as neural networks, control systems, meteorological systems, biological systems and so on in the natural world. Thus,
the investigation of the stability in such time-delayed systems is important [4]. The generation of chaos has been reported inall self excited oscillation systems containing a time delay [5]. The oscillators have feedback systems which control gains inthis study. Such a chaotic circuit can be easily realized by using a simple electric circuit element and can be analyzed exactly.
The coupling switch connects alternately with one subcircuit and other with a fixed time interval. On the other hand, there areexamples of nonlinear phenomena, chaotic synchronization and so on [6]. In particular, many studies on the synchronizationof coupled chaotic circuits have been reported [7].
In this study, we devise the novel coupling method that takes advantage of the features of time-delayed chaotic circuits.
The novel coupled method utilizes the characteristics of circuits having time-delayed feedback. Then, we observe switching
the synchronization state. We carry out computer calculations for three coupled auto gain controlled oscillators and investigate
time-delayed subcircuits effects a change of the synchronization state and the time waveform. The switching synchronization
state is changed by each time-delayed subcircuit. We focus on relationships between the switching synchronization state andthe pattern of time delay. Moreover, we investigate the cycle of the switching synchronization state.
R EFERENCES[1] G. Abramson, V. M. Kenkre and A. R. Bishop, “Analytic Solutions for Nonlinear Waves in Coupled Reactig Systems,”
Physical A: Statistial Mechanics and its Applications, vol. 305, no.3-4, pp. 427-436, 2002.
[2] C. M. Gray, “Synchronization Oscillators in Neural Systems: Mechanisms and Functions,” J. Computational Neuroscience,
vol. 1, pp. 11-38, Feb. 1994.
[3] Y. Zhang, G. H. Du and J. J. Jiang, “Synchronization Chaos by Impulsive Feedback Method,” International Jounal ofbifurcation and Chaos, vol. 11, no.8, pp. 2233-2243, 2001.
[4] X. Liu, “Stability of impulsive control systems with time delay. Mathematical and Computer Modelling,” Vol.39, pp.511519, 2004.
[5] T. Maruyama, N. Inaba, Y. Nishio and S. Mori, “Chaos in an Auto Gain Controlled Oscillator Containing Time Delay,”
Trans. IEICE, vol. J 72-A, pp. 1814-1820, Nov. 1989.
[6] T. Maruyama, N. Inaba, Y. Nishio and S. Mori, “Chaos in Self Oscillator Circuit Containing Time Delay,” Proceedings ofIEEE Midwest Symposium on Circuits and Systems (MWSCAS’90), vol. 2, pp. 1055-1058, Aug. 1990.
[7] L. M. Pecora and T. L. Carroll, “Synchronization in Chaotic Systems,” Physical Review Letters, vol. 64, no.8, pp. 821-824,Feb. 1990.