Volume 120, Number 5, December 2017
|Number of page(s)||7|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||23 February 2018|
Rare events in networks with internal and external noise
U.S. Naval Research Laboratory, Code 6792, Plasma Physics Division - Washington, DC, USA
Received: 19 December 2017
Accepted: 2 February 2018
We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and time scale of rare events are considered in detail for extinction in the Susceptible-Infected-Susceptible model as an illustration. We find that when both types of noise are present, there is a crossover region as the network size is increased, where the probability exponent for large deviations no longer increases linearly with the network size. We demonstrate that the form of the crossover depends on whether the endemic state is localized near the epidemic threshold or not.
PACS: 64.60.aq – Networks / 05.45.-a – Nonlinear dynamics and chaos / 87.23.Cc – Population dynamics and ecological pattern formation
© EPLA, 2018
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