Effects of asymmetric rates and impulse interference in Rock-Paper-Scissors games

Abstract

The dynamics of systems composed of cyclically competing species are complicated by the fact that they are strongly influenced by fluctuations. For this reason, it is attractive to study low-dimensional cycles where these impacts are most prominent. In this paper, we investigate the impacts of asymmetric compared to symmetric reactive rates on three-species biological diversity and spatial pattern formation in a four-state case using an RPS game model on a one-dimensional lattice. In addition, we also discuss the effects of interference thresholds on biodiversity maintenance when species are impulsively disturbed under both symmetric and asymmetric rates. The results show that enhancement of the competition rate promotes biodiversity while the mobility rate has the opposite effect when these rates being symmetric. Meanwhile, changes in reproductive rates have no direct effect on biodiversity. If rates are asymmetric, only one species survives and biodiversity is negatively affected. Conversely, the outcome of single species survival is altered when species are impulsively disturbed. Under symmetric rates, an increase in interference threshold results in a shift from coexistence of three species to survival of two species. With asymmetric rates, population dynamics change from the survival of only one species to the survival of two species if the interference is introduced. Our findings may enlighten people by RPS game model to protect endangered animals, or kill off harmful species, or to engineer cyclical population to stabilize the functionality of gene circuits for cancer treatment, or to guide election campaign.