New Solutions in Three Species Cyclic Competition Models

Models of competing species within ecological communities, can provide insight into the fundamentals of biological sustainability and are thus valuable in understanding the origins and the development of life. We consider three-species cyclic models, where each species wins one competition and loses the other, analogous to the children's game of Rock-Paper-Scissors (RPS). Classical RPS competition models are known to have two regimes, (i) stable coexistence of all three species and (ii) a heteroclinic cycle of alternating, progressively longer, periods of dominance for each species. We propose that adding a saturation term in the inter-species competition can significantly effect the outcome of the competition. By considering models with a saturation term, we find a new periodic solution (Hopf regime) between these two regimes.