2019/08/12 by Leonid Bunimovich, DJ Passey, D. J. Passey +2 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Dynamic network analysis #Dynamics (music) #Hierarchical network model #Modular design #Network dynamics #Network topology #Neural Networks Stability and Synchronization #Neural Networks and Applications #Process (computing) #Topology (electrical circuits) #Type (biology) #math.DS #math.SP #msc:05C82 #msc:37C75 #msc:47J10 #nlin.AO
paper · pdf · doi:10.1142/s0218127420500911
published in International Journal of Bifurcation and Chaos 30(06), 2050091 (World Scientific) · 40 pages, 8 figures
arxiv created 2019/08/12 · openalex created_date 2019/08/22 · openalex publication_date 2020/05/01 · arxiv updated 2020/06/24 · openalex updated_date 2026/08/06
One of the hallmarks of real networks is the ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the function(s) they perform. A recent model of network growth based on this notion of specialization has been able to reproduce some of the most well-known topological features found in real-world networks including right-skewed degree distributions, the small world property, modular as well as hierarchical topology, etc. Here we describe how specialization under this model also effects the spectral properties of a network. This allows us to give the conditions under which a network is able to maintain its dynamics as its topology evolves. Specifically, we show that if a network is intrinsically stable, which is a stronger version of the standard notion of global stability, then the network maintains this type of dynamics as the network evolves. This is one of the first steps toward unifying the rigorous study of the two types of dynamics exhibited by networks. These are the dynamics of a network, which is the topological evolution of the network’s structure, modeled here by the process of network specialization, and the dynamics on a network, which is the changing state of the network elements, where the type of dynamics we consider is global stability. The main examples we apply our results to are recurrent neural networks, which are the basis of certain types of machine learning algorithms.