Converting high-dimensional complex networks to lower-dimensional ones preserving synchronization features

Abstract

Studying the stability of synchronization of coupled oscillators is one of the prominent topics in network science. However, in most cases, the computational cost of complex network analysis is challenging because they consist of a large number of nodes. This study includes overcoming this obstacle by presenting a method for reducing the dimension of a large-scale network, while keeping the complete region of stable synchronization unchanged. To this aim, the first and last non-zero eigenvalues of the Laplacian matrix of a large network are preserved using the eigen-decomposition method and, Gram-Schmidt orthogonalization. The method is only applicable to undirected networks and the result is a weighted undirected network with smaller size. The reduction method is studied in a large-scale a small-world network of Sprott-B oscillators. The results show that the trend of the synchronization error is well maintained after node reduction for different coupling schemes.

Dynamical Analysis and Synchronization of a New Memristive Chialvo Neuron Model

“…Hence, the networks of continuous neural models are time-consuming, especially when coupled in a high-dimensional network or higher-order one [11,12]. Even though some reduction methods reduce the cost of analyzing a high-dimensional network of oscillations [13], map-based models are generally faster and more efficient for analyzing large networks.…”