Study of Self-Organization Phenomena in the System Consisting of Activity-Doped Elements

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The discrete chemical oscillator has been obtained by localizing the BZ reaction on the surface of the cation exchange beads. This can be regarded as one of the non-equilibrium system consisting of activity-doped elements.These coupled oscillators are peculiar compared with those of CSTR.Entrained states of 1 : n or n : 1 are very stable. In particular, the transition between 1 : 1 and 1 : 2 (or 2 : 1) was necessarily accompanied by an irregular oscillation. This irregular behavior was found to be chaotic by checking the power spectrum, the three dimensional reconstructed attractor, and the largest Lyapunov exponent. In the case of three coupled oscillators, both clockwise and counterclockwise rotation modes were observed, and furthermore the transition between those modes was also observed. It is considered that the appearance of the rotation mode is due to the compensation effect for a frustration as found in the coupled Ising spin system.Various self-organization phenomena were induced by electric fields. Sensitive responses to electric fields result from that most of chemical species relevant to the wave propagation are ionic. The phase diagram concerning responses of the oscillator was obtained as a function of the frequency and the strength of the electric field ; (1) entrained states of 1/1,1/2 and 2/1 is dominant in the whole diagram, (2) for a low electric field, the boundary regions between these region are occupied by carious harmonic state following the Farey's tree and the quasiperiodic oscillation, (3) the transition from 1/1 to 2/1 or 1/2 entrainments must necessarily occur crossing a chaotic state, (4) the features of the phase diagram well resemble those of the biological cells. Effects of electric fields on the chemical oscillator were explained by a voltage-dependent spatial distribution of Br.