Huang Liang, Chen Qingfei, Lai Ying-Cheng, Pecora Louis M
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 2):036204. doi: 10.1103/PhysRevE.80.036204. Epub 2009 Sep 15.
Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators. We address this issue by examining, systematically, MSFs for known chaotic oscillators. Our computations and analysis indicate that it is generic for MSFs being negative in a finite interval of a normalized coupling parameter. A general scheme is proposed to classify the typical behaviors of MSFs into four categories. These results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators.
主稳定性函数（MSFs）是复杂动力系统同步研究的基础。例如，对于耦合振子网络，同步发生的一个必要条件是在相应归一化耦合参数下的主稳定性函数为负。了解各种混沌振子的主稳定性函数的典型行为是预测这些振子网络集体动力学的关键。我们通过系统地研究已知混沌振子的主稳定性函数来解决这个问题。我们的计算和分析表明，在归一化耦合参数的有限区间内主稳定性函数为负是普遍现象。提出了一种将主稳定性函数的典型行为分为四类的通用方案。这些结果通过对实际耦合振子网络同步动力学的直接模拟得到了验证。
