Open AccessQuasi-stationary oscillations in game-driven evolutionary dynamics
Author(s) -
O. S. Vershinina,
Mikhail Ivanchenko,
С. В. Денисов
Publication year - 2019
Publication title -
cybernetics and physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 8
eISSN - 2226-4116
pISSN - 2223-7038
DOI - 10.35470/2226-4116-2019-8-4-307-311
Subject(s) - stationary distribution , stationary state , statistical physics , limit (mathematics) , nonlinear system , population , limit cycle , dynamics (music) , distribution (mathematics) , mathematics , state (computer science) , computer science , physics , mathematical analysis , statistics , demography , algorithm , quantum mechanics , sociology , markov chain , acoustics
Nonlinear dynamics makes use of attactors to describe asymptotic behavior of complex systems. However, in real life can be unattainable, as achieving them might require time much exceeding all relevant timescales of a system. Therefore, there is an increasing interest in quasi-stationary states, where the system rapidly converges to and remains for a long time, before getting into an absorbing (asymptotic) state. Exemplifying in the famous Dawkins‘ Battle of the Sexes game, we demonstrate that quasi-stationary distributions can produce not simply different, but a much more complex behavior, then the asymptotic ones, that is transient self-sustained oscillations of player numbers and the corresponding non-unimodal probability distribution. We find that parameters of the quasi-stationary limit cycle depend on the population size.