Dynamics of a cluster of chaotic oscillators on a network are studied using coupled maps. By introducing the association schemes, we obtain coupling strength in the adjacency matrices form, which satisfies Markov matrices property. We remark that in general, the stability region of the cluster of oscillators at the synchronization state is characterized by Lyapunov exponent which can be defined based on the N-coupled map. As a detailed physical example, dynamics of microbubble cluster in an ultrasonic field are studied using coupled maps. Microbubble cluster dynamics have an indicative highly active nonlinear phenomenon, were not easy to be explained. In this paper, a cluster of microbubbles with a thin elastic shell based on the modified Keller-Herring equation in an ultrasonic field is demonstrated in the framework of the globally coupled map. On the other hand, a relation between the microbubble elements is replaced by a relation between the vertices. Based on this method, the stability region of microbubbles pulsations at complete synchronization state has been obtained analytically. In this way, distances between microbubbles as coupling strength play the crucial role. In the stability region, we thus observe that the problem of study of dynamics of N-microbubble oscillators reduce to that of a single microbubble. Therefore, the important parameters of the isolated microbubble such as applied pressure, driving frequency and the initial radius have effective behavior on the synchronization state.

使用耦合映射图研究网络上混沌振荡器簇的动力学。通过引入关联方案，我们以邻接矩阵形式获得了满足马尔可夫矩阵性质的耦合强度。我们注意到，一般而言，振荡器簇在同步状态下的稳定区域的特征在于李雅普诺夫指数，该指数可以基于N耦合图。作为详细的物理示例，使用耦合图研究了超声场中微泡团簇的动力学。微气泡团簇动力学具有指示性的高度活跃的非线性现象，不容易解释。在全局耦合图的框架中，基于超声场中的改进的Keller-Herring方程，证明了具有薄弹性壳的微气泡簇。另一方面，微泡元件之间的关系被顶点之间的关系所代替。基于此方法，已经获得了完全同步状态下微气泡脉动的稳定区域。这样，微泡之间的距离作为耦合强度起着至关重要的作用。在稳定区域，N-微泡振荡器减少到单个微泡的振荡器。因此，孤立的微气泡的重要参数，例如施加的压力，驱动频率和初始半径，在同步状态下具有有效的行为。