López-Ruiz R, Moreno Y, Pacheco A F, Boccaletti S, Hwang D-U
Departament of Computer Science and BIFI, Faculty of Sciences, University of Zaragoza, 50009, Zaragoza, Spain.
Neural Netw. 2007 Jan;20(1):102-8. doi: 10.1016/j.neunet.2006.04.002. Epub 2006 Jun 23.
A network with a logistic-like local dynamics is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small, the dynamics is dissipated and there is no activity: the network is turned off. For a critical value of the coupling, a non-null stable synchronized state, which represents a turned on network, emerges. This global bifurcation is independent of the network topology. We characterize the bistability of the system by studying how to perform the transition, which is now topology dependent, from the active state to that with no activity, for the particular case of a scale-free network. This could be a naive model for the wakening and sleeping of a brain-like system, i.e., a multi-component system with two different dynamical behaviors.
考虑一个具有类似逻辑斯蒂局部动力学的网络。我们在最近邻节点之间实现了平均场乘法耦合。当耦合参数较小时，动力学是耗散的且没有活动：网络处于关闭状态。对于耦合的一个临界值，出现了一个非零稳定同步状态，它代表一个开启的网络。这种全局分岔与网络拓扑无关。对于无标度网络的特殊情况，我们通过研究如何执行从活动状态到无活动状态的转变（现在这种转变依赖于拓扑）来刻画系统的双稳性。这可能是一个关于类脑系统（即具有两种不同动力学行为的多组分系统）唤醒和睡眠的简单模型。
