Chaotic oscillations via quasi-periodicity caused by applying external modulation in ionization waves

Takao Fukuyama, Ruslan Kozakov1), Holger Testrich1), Christian Wilke1), Yoshinobu Kawai

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University,
Kasuga-kouen 6-1, Kasuga, Fukuoka 816-8580, Japan
1)Max-Planck-Institut für Plasmaphysik, Teilinstitut Greifswald,
Wendelsteinstrasse 1, D-17491 Greifswald, Germany

Dynamical behavior of nonlinear ionization waves excited in positive columns of glow discharge is investigated with external modulation. In dissipative physical systems, such as occur in plasmas, fluids, chemicals etc., it is often observed that the system settles into a state of sustained chaotic motion. Chaos has been observed in various physical systems and several routs to chaos have been identified. Ionization waves in glow discharge are a typical nonlinear dynamical system with a large number of degrees of freedom, and it is of interest as a medium for testing the universal characteristics of chaos such as the low-dimensional behavior and certain route to chaos[1]. It is well known that competition of two frequencies leads the system into a state of chaotic motion via quasi-periodicity as mentioned in Ruelle and Takens scenario[2], Curry and Yorke theory[3]. Here, quasi-periodic route to chaos is investigated experimentally in ionization waves. The wave property can be mainly controlled by discharge current and pressure, and it can be classified into three type of coherent striations, which are P wave, S wave, and R wave. Periodic modulation is superimposed to the discharge current, when the system is in R wave regime which shows coherent striation. Quasi-periodicity with two frequencies is realized by competition between self-sustained R wave and external periodic modulation. According to the change of the rate of discharge current modulation, the system comes to show chaotic oscillations via quasi-periodicity.

References

[1]K. Ohe, Current Topics in the Phys. Fluids 1 (1994) 319.
[2]D. Ruelle and F. Takens, Commun. Math. Phys. 20 (1971) 167.
[3]J. H. Curry and J. A. Yorke, Lect. Notes Math. 668 (1978) 48.