Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system

¹ Departamento de Física, Universidade Federal da Paraíba - 58051-970 João Pessoa, PB, Brazi
² Departamento de Física, Universidade Estadual de Maringá - 87020-900 Maringá, PR, Brazil
³ Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences P.O. Box 49, H-1525 Budapest, Hungary

Received: 18 November 2018
Accepted: 5 December 2018

Abstract

Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly new situation emerges if we introduce an apex predator who can be superior to all members of the mentioned three-species system. In the latter case the evolution may terminate into three qualitatively different destinations depending on the apex predator decaying ratio q. In particular, the whole population goes extinct or all four species survive or only the original three-species system remains alive as we vary the control parameter. These solutions are separated by a discontinuous and a continuous phase transitions at critical q values. Our results highlight that cyclic dominant competition can offer a stable way to survive even in a predator-prey–like system that can be maintained for large interval of critical parameter values.