Aguirre Luis A, Portes Leonardo L, Letellier Christophe
Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais, Belo Horizonte 31.270-901, Minas Gerais, Brazil.
Programa de Pós-Graduação em Engenharia Elétrica da Universidade Federal de Minas Gerais-Av. Antônio Carlos 6627, 31.270-901 Belo Horizonte, Minas Gerais, Brazil.
Chaos. 2017 Oct;27(10):103103. doi: 10.1063/1.4985291.
Observability is the property that enables recovering the state of a dynamical system from a reduced number of measured variables. In high-dimensional systems, it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. The observability of a network of neuron models depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, to perform a study of observability using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, to study the emergence of phase synchronization in networks composed of neuron models. This is done performing multivariate singular spectrum analysis which, to the best of the authors' knowledge, has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization: (i) without having to measure all the state variables, but only one (that provides greatest observability) from each node and (ii) without having to estimate the phase.
可观测性是一种属性，它能够从数量减少的测量变量中恢复动态系统的状态。因此，在高维系统中，确保用于执行分析所记录的变量能够很好地反映系统动态的可观测性非常重要。神经元模型网络的可观测性不仅非平凡地取决于节点动态的可观测性，还取决于网络的拓扑结构。本文的目的有两个。第一，通过计算三种不同的可观测性系数，使用四个著名的神经元模型进行可观测性研究。这不仅阐明了模型的可观测性属性，还展示了在这类模型的背景下每种类型系数适用的局限性。第二，研究由神经元模型组成的网络中相位同步的出现。这是通过执行多变量奇异谱分析来完成的，据作者所知，该分析尚未在神经元模型网络的背景下使用。结果表明，可以检测到相位同步：（i）无需测量所有状态变量，而只需从每个节点测量一个（提供最大可观测性的变量）；（ii）无需估计相位。
