del Genio Charo I, Romance Miguel, Criado Regino, Boccaletti Stefano
School of Life Sciences, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom.
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062819. doi: 10.1103/PhysRevE.92.062819. Epub 2015 Dec 15.
We provide a rigorous solution to the problem of constructing a structural evolution for a network of coupled identical dynamical units that switches between specified topologies without constraints on their structure. The evolution of the structure is determined indirectly from a carefully built transformation of the eigenvector matrices of the coupling Laplacians, which are guaranteed to change smoothly in time. In turn, this allows one to extend the master stability function formalism, which can be used to assess the stability of a synchronized state. This approach is independent from the particular topologies that the network visits, and is not restricted to commuting structures. Also, it does not depend on the time scale of the evolution, which can be faster than, comparable to, or even secular with respect to the dynamics of the units.
我们为耦合相同动态单元网络的结构演化问题提供了一种严格的解决方案，该网络在特定拓扑之间切换且对其结构无限制。结构的演化是通过对耦合拉普拉斯算子特征向量矩阵进行精心构建的变换间接确定的，这些变换保证随时间平滑变化。反过来，这使得人们能够扩展主稳定性函数形式体系，该体系可用于评估同步状态的稳定性。这种方法独立于网络所经历的特定拓扑，并且不限于可交换结构。此外，它不依赖于演化的时间尺度，该时间尺度相对于单元的动力学可以更快、相当或甚至是长期的。
