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DY: Fachverband Dynamik und Statistische Physik
DY 20: Networks: From Topology to Dynamics I (joint session SOE/DY)
DY 20.3: Talk
Tuesday, March 28, 2023, 11:30–11:45, ZEU 260
Analytical methods to stochastic binary-state dynamics on networks. — •Antonio Fernandez Peralta1 and Raul Toral2 — 1Central European University, Vienna, Austria — 2IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), Palma de Mallorca, Spain
Recently, there has been a lot of effort in the development of highly accurate mathematical descriptions of the dynamics of binary-state models defined on complex networks. There are two main approaches: (i) individual based-approaches where the variables are the state of each node, and (ii) compartmental approaches where nodes are aggregated based on some topological property such as, for example, the number of neighbors in the network. Except in a few cases where stochastic effects are taken into account at some extent, the approaches are usually followed by a deterministic description, neglecting the stochastic nature of the models defined by the individual transitions rates. Stochastic effects may become relevant even for extremely large system sizes, specially if the system is close to a critical point, or the network has high degree heterogeneity. Besides, there are some models where the deterministic approach does not provide the relevant information sought. For instance, the noisy-voter (Kirman) model, the contact process or the Threshold model, are examples of relevance in which the stochastic effects greatly dominate the dynamics. The main aim of this work is to give a general theoretical approach to binary-state models on complex networks that takes into account stochastic effects, going beyond incomplete deterministic approaches.