Nonlinearity + Networks: A 2020 Vision

TL;DR

This paper surveys key topics at the intersection of nonlinearity and networks, emphasizing emerging areas like temporal, adaptive, and higher-order networks, and their applications in various dynamical processes.

Contribution

It provides a comprehensive overview of recent advances and highlights promising directions in the study of nonlinear network dynamics and structures.

Findings

Temporal networks reveal time-dependent interaction patterns.

Adaptive networks couple structure evolution with dynamics.

Higher-order interactions involve complex multi-entity relationships.

Abstract

I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics include temporal networks (in which the entities and/or their interactions change in time), stochastic and deterministic dynamical processes on networks, adaptive networks (in which a dynamical process on a network is coupled to dynamics of network structure), and network structure and dynamics that include "higher-order" interactions (which involve three or more entities in a network). I draw examples from a variety of scenarios, including contagion dynamics, opinion models, waves, and coupled oscillators.