2015 Taiwan and Japan Conference on Circuits and Systems
Shikoku University Plaza, Tokushima, Japan. August 19-21, 2015

Synchronization State of Coupled
Chaotic Circuits with Changing Time DelaySeiya 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 UMMARYIn the natural world there are many nonlinear systems containing time delay, such as neural networks, control systems,
meteorological systems, biological systems and so on. Namely, stability of such delay systems is important to elucidate
these phenomena [1]. Generation of chaos of them all is reported self excited oscillation system containing time delay. Thischaotic circuit can be easily realized by using simple electric circuit element and analyzed exactly [2]. There are examplesof nonlinear phenomena, chaotic synchronization, clustering phenomenon and so on [3]. In particular, a number of studies on
synchronization of coupled chaotic circuits have been made [4]. In previous study, we have investigated synchronization state
observed in coupled time delayed chaotic circuits by inductor [5]. Coupled nonlinear circuits by inductor can be observed
in-phase and anti-phase synchronization states [6][7]. As a result, two types of synchronization state is caused by increasing thechaotic strength of subcircuit. In roughly divided, two types of synchronization states depending on initial values and numberof subcircuits can be observed. Moreover, synchronization state can be classified by the number of coupled chaotic circuit
whether the number is even or odd.
In this study, we investigate synchronization states observed in coupled chaotic circuits with time delay by inductor. Timedelay of chaotic circuit depends types of attractor. We focus on relationships between synchronization state and time delay.
Single type synchronization state can be observed by changing time delay of subcircuits. Coexisting synchronization states
depending on the initial values can be observed in specific time delay values. By carrying out computer simulations, weinvestigate the effect of various time delay values on the subcircuit to changing synchronization states.
R EFERENCES[1] X. Liu, “Stability of impulsive control systems with time delay. Mathematical and Computer Modelling,” Vol.39, pp.511-519, 2004.
[2] 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.
[3] T. Maruyama, N. Inaba, Y. Nishio and S. Mori, “Chaos in Self Oscillator Circuit Containing Time Delay,” Proceedings of IEEE Midwest Symposium on
Circuits and Systems (MWSCAS’90), vol. 2, pp. 1055-1058, Aug. 1990.
[4] L. M. Pecora and T. L. Carroll, “Synchronization in Chaotic Systems,” Physical Review Letters, vol. 64, no.8, pp. 821-824, Feb. 1990.
[5] S. Kita, Y. Uwate and Y. Nishio, “Synchronization State of Coupled Chaotic Circuits Containing Time Delay,” Proc. NOMA’15 (accepted).
[6] M. Wada, Y. Nishio and A. Ushida, “Analysis of Bifurcation Phenomena in Two Chaotic Circuits Coupled by an Inductor,” IEICE Transactions on
Fundamentals, vol. E80-A, no. 5, pp. 869-875, May. 1997.
[7] M. Wada, Y. Nishio and A. Ushida, “Wave Propagation Phenomena of Phase States in Oscillators Coupled by Inductors as a Ladder,” IEICE Transactions
on Fundamentals, vol. E82-A, no. 11, pp. 2592-2598, Nov. 1999.

- 33 -