Oscillations and synchronization in SIRS models of epidemic propagations
Alexey Shabunin, Saratov State University, Russia
Abstract
Aim: Study of synchronization of oscillations in ensembles of probabilistic cellular automata that simulate the spread of infections in biological populations.
The research conideres synchronization of oscillations between lattices of cellular automata, which model propagation of infections in biological populations.
In the result of the investigation effect of synchronization of irregular oscillations, similar to the phenomenon of synchronization of chaos in dynamical systems, has been found. It is shown that the coupled lattices of cellular automata can demonstrate the effect of phase locking, as well as the tuning of the main frequencies in the oscillation spectra; at strong coupling they also can demonstrate an almost complete synchronization regime.
The most interesting result of the work is the revealed similarity of the phenomenon of chaos synchronization, which is well known for deterministic systems, with synchronization of irregular oscillations in interacting stochastic ensembles, whose behavior is determined exclusively by probabilistic laws. At the same time, the interaction algorithm, which has been used in the modeling is too idealized, becouse it does not consider the finite speed of diffusion processes. Taking the last into account will probably lead to more complex types of synchronization that has been found in the research.
Speaker
Alexey Shabunin
Professor of Saratov State University
Russia
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