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

将BZ反应定域在阳离子交换小球表面，得到了分立的化学振子。这可以看作是一种由活性掺杂元素组成的非平衡体系，与CSTR相比，这种耦合振子是特殊的。特别是，1：1和1：2(或2：1)之间的过渡必然伴随着不规则的振荡。通过检查功率谱、三维重构吸引子和最大Lyapunov指数，发现这种不规则行为是混沌的。在三个耦合振子的情况下，观察到了顺时针和逆时针两种转动模式，并且还观察到了这些模式之间的跃迁。认为旋转模的出现是由于耦合伊辛自旋系统中的受挫补偿效应所致，电场诱导了各种自组织现象。由于与波传播相关的大多数化学物质都是离子的，所以对电场的敏感响应。得到了振子响应随频率和电场强度变化的相图：(1)在整个相图中，1/1、1/2和2/1的夹带状态占主导地位；(2)对于低电场，这些区域之间的边界区域被遵循Farey树和准周期振荡的各种简谐态占据；(3)从1/1到2/1或1/2夹带的转变必然发生在一个混沌态上，(4)相图的特征与生物细胞的特征非常相似。用BR随电压变化的空间分布解释了电场对化学振荡器的影响。

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.