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珠表面，得到了离散化学振子。这可以看作是由活性掺杂元素组成的非平衡体系之一。这些耦合振荡器与CSTR相比是特殊的。1: n或n: 1的夹带态是非常稳定的。特别地，在1:1和2:1（或2:1）之间的过渡必然伴随着不规则的振荡。通过对功率谱、三维重构吸引子和最大Lyapunov指数的检验，发现这种不规则行为是混沌的。在三个耦合振子的情况下，观察到顺时针和逆时针的旋转模式，并进一步观察到这些模式之间的转换。认为旋转模式的出现是由于在耦合的伊辛自旋系统中发现的对挫折的补偿效应。电场诱导了各种自组织现象。对电场的敏感反应是由于大多数与波传播有关的化学物质都是离子。得到了谐振子响应随电场强度和频率变化的相图；(1) 1/1,1/2和2/1夹带态在整个图中占主导地位；(2)对于低电场，这些区域之间的边界区域被各种谐波状态所占据，遵循Farey树和准周期振荡；(3)从1/1到2/1或1/2夹带态的过渡必须发生在混沌状态中；(4)相图的特征与生物细胞的特征很相似。电场对化学振子的影响由Br的电压依赖性空间分布来解释。

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.