School of Mathematics and Statistics, Wuhan University, Hubei 430072, China.
Chaos. 2011 Dec;21(4):043129. doi: 10.1063/1.3664396.
How to recover the underlying connection topology of a complex network from observed time series of a component variable of each node subject to random perturbations is studied. A new technique termed Piecewise Granger Causality is proposed. The validity of the new approach is illustrated with two FitzHugh-Nagumo neurobiological networks by only observing the membrane potential of each neuron, where the neurons are coupled linearly and nonlinearly, respectively. Comparison with the traditional Granger causality test is performed, and it is found that the new approach outperforms the traditional one. The impact of the network coupling strength and the noise intensity, as well as the data length of each partition of the time series, is further analyzed in detail. Finally, an application to a network composed of coupled chaotic Rössler systems is provided for further validation of the new method.
研究了如何从受随机扰动的每个节点的一个分量变量的观测时间序列中恢复复杂网络的基础连接拓扑。提出了一种新的技术，称为分段格兰杰因果关系。通过仅观察每个神经元的膜电位，分别对两个 FitzHugh-Nagumo 神经生物学网络进行了新方法的有效性说明，其中神经元分别线性和非线性耦合。与传统的格兰杰因果关系检验进行了比较，发现新方法优于传统方法。进一步详细分析了网络耦合强度和噪声强度以及时间序列每个分区数据长度的影响。最后，提供了一个由耦合混沌 Rossler 系统组成的网络的应用，以进一步验证新方法。
