Skardal Per Sebastian, Arenas Alex
Department of Mathematics, Trinity College, Hartford, CT 06106, USA. ; Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain.
Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain.
Sci Adv. 2015 Aug 21;1(7):e1500339. doi: 10.1126/sciadv.1500339. eCollection 2015 Aug.
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
复杂系统和网络耦合动力系统的控制是数学和物理学中具有至关重要理论意义的主题，在工程学和其他各类科学中有着广泛应用。受近期对智能电网技术研究的推动，我们研究同步控制，并考虑具有非线性相互作用的耦合相位振子网络这一重要情形——这是一个数十年来一直引导我们理解自组织的典型示例。我们开发了一种基于识别和稳定有问题振子的控制方法，从而得到一个稳定的特征值谱，进而得到一个线性稳定的同步状态。稳定网络所需的控制量，即振子数量，主要由网络的耦合强度、动态异质性和平均度决定，而几乎不依赖于网络本身的结构异质性。
