Design of functional network dynamics and universality

我们设计振荡器网络，通过对其连接进行适当的重新布线来改善同步特性。我们考虑对于给定的连接总数而言，最佳的网络架构是什么。从振荡器的初始随机网络开始，通过使用马尔科夫链蒙特卡罗方法适当地重新布线元件之间的链接，可以大大提高其自主同步能力。这种最优网络的体系结构强烈地依赖于约束，例如可用链路的总数。通过对网络进行适当的重新布线，可以在同步信号中获得较强的增益。结果还表明，在存在噪声的情况下，导致相同振子群的最佳同步的结构与无噪声的异类振子群的最优同步结构有本质上的不同。得到了大量的优化网络系综，并研究了它们的统计性质。这些结果发表在《物理》杂志上。Rev.E.

We design the network of oscillators to improve synchronization properties through appropriate rewiring of its connections. We consider what are the optimal network architectures for a given total number of connections. Starting with an initial random network of oscillators, its autonomous synchronization ability can be largely improved by appropriately rewiring the links between the elements using the Markov chain Monte Carlo method. The architectures of such optimal networks strongly depend on the constraints, such as the total number of links available. Through the appropriate rewiring of a network, a strong gain in the synchronization signal can be achieved. It is also shown that the architectures leading to the improved synchronization of identical oscillators in the presence of noise are essentially different from the optimal synchronization architectures for heterogeneous oscillator populations without noise. Large ensembles of optimized networks are obtained and their statistical properties have been investigated. These results are published in Phys. Rev. E.