中文摘要：

松弛型基因随机振子是三类基因振子（光滑振子、松弛振子和随机振子）中的一种．具有相抑制耦合细胞通信的这种类基因振子的同步与聚类是一个有趣且令人关注的问题。这里，数值模拟显示出振子之间的相差分布能够展示出单峰、双峰或多峰分布，但依赖于噪声强度和细胞密度。而且，数值地发现存在细胞数目的一个阈值，当细胞数目超过此阈值时，对于任意的噪声强度相差分布函数的峰值性几乎保持不变。这些结果表明抑制耦合的松弛型随机振子具有不同于普通耦合的光滑或松弛振子的同步与聚类机制。

英文摘要：

Relaxation type genetic stochastic oscillators are a particular one of three classes of genetic oscillators （smooth.relaxation and stochastic oscillators ）. Synchronization and cluster of an ensemble of genetic oscillators of this type via phase-repulsive cell-to-cell communication are an interesting yet attending question. Here, the numerical simulation demonstrate that the distribution of phase differences among the stochastic oscillators can display such characteristics as unimodality, bimodality or polymodality, depending on both noise intensity and cell number. Moreover, it was numerically found there is a threshold of the cell number, the modality of phase difference distribution almost keeps invariant for arbitrary noise intensities as the cell number is beyond the threshold. These results indicate that the repulsively coupled relaxation-type stochastic oscillators have the mechanism of synchronization and cluster different from that of commonly coupled smooth or relaxation oscillators.