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

• Main Authors: Barna Garay, Judit Várdai
• Format: Article
• Language: English
• Published: University of Szeged 2018-06-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: consensus dynamics; periodic orbits; monotone maps; graph eigenvectors; ordinal patterns
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=6826

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.