Moving average network examples for asymptotically stable periodic orbits of monotone maps

Abstract

For a certain type of discrete-time nonlinear consensus dynamics, asymptotically stable periodic orbits are constructed. Based on a simple ordinal pattern assumption, the Frucht graph, two Petersen septets, hypercubes, a technical class of circulant graphs (containing Paley graphs of prime order), and complete graphs are considered – they are all carrying moving average monotone dynamics admitting asymptotically stable periodic orbits with period $2$. Carried by a directed graph with $594$ (multiple and multiple loop) edges on $3$ vertices, also the existence of asymptotically stable $r$-periodic orbits, $r=3,4,\ldots$ is shown.

Keywords

• consensus dynamics
• periodic orbits
• monotone maps
• graph eigenvectors
• ordinal patterns