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Emergence of cascades in the linear and nonlinear Hawkes processes

Banff International Research Station for Mathematical Innovation and Discovery

The self-exciting systems as represented by neural networks are known to exhibit catastrophic chain reaction if the internal interaction exceeds an epidemic threshold. Recently, we have shown that the same systems may exhibit nonstationary fluctuations already in the subthreshold regime [1,2]; cascades of events or spikes may emerge in the Hawkes process even in the absence of external forcing. In a practical situation, however, systems are subject to time-varying environment in addition to internal interaction between elements. Here we attempt to estimate the degree in which the nonstationary fluctuations occurring in the system are induced by external forcing or internal interaction. [1] T. Onaga and S. Shinomoto, Bursting transition in a linear self-exciting point process. Physical Review E (2014) 89:042817. [2] T. Onaga and S. Shinomoto, Emergence of event cascades in inhomogeneous networks. Scientific Reports (2016) 6:33321.

Mathematics; Statistics; Probability theory and stochastic processes; Applied statistics

video/mp4

Author affiliation: Kyoto University

2019-03-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68547

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/