Anca Rǎdulescu, Danae Evans, Amani-Dasia Augustin, Anthony Cooper, Johan Nakuci, Sarah Muldoon
Synchronization and clustering are well studied in the context of networks of oscillators, such as neuronal networks. However, this relationship is notoriously difficult to approach mathematically in natural, complex networks. Here, we aim to understand it in a canonical framework, using complex quadratic node dynamics, coupled in networks that we call complex quadratic networks (CQNs). We review previously defined extensions of the Mandelbrot and Julia sets for networks, focusing on the behavior of the node-wise projections of these sets and on describing the phenomena of node clustering and synchronization...
November 22, 2023: Neural Computation