Metastable oscillations in an evolutionary game: Synchronization and control

Abstract

Evolutionary games with a finite number of players may manifest transient oscillatory dynamics before reaching an absorbing state. Such oscillations could be prone to synchronization, however its details and specific properties are not known. Here, we investigate synchronization of metastable oscillations in the finite-dimensional evolutionary game “Battle of the Sexes”, as well as the possibility of controlling the properties of these oscillations by a multiplicative periodic signal. The appropriately generalized frequency and phase quantifiers demonstrate the possibility of synchronization, and the asymmetry of frequency range, induced by the finite size of population. Evolution of oscillations under strengthening periodic driving depends on whether synchronization is reached: in the synchronous regime the amplitude of oscillations grows, while their lifetime decreases, whereas in the asynchronous regime their amplitude decays to zero with the quasi-stationary distribution becoming unimodal.