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

Garay, Barnabás M. and Várdai, Judit: Moving average network examples for asymptotically stable periodic orbits of monotone maps. Electronic journal of qualitative theory of differential equations 52. pp. 1-18. (2018)

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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, . . . is shown.

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