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arXiv · 1812.03406

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

D. Bazeia·B. F. de Oliveira·A. Szolnoki
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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 superior 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.

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D. Bazeia, B. F. de Oliveira, A. Szolnoki. 2018-12-08. Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system. https://doi.org/10.1209/0295-5075%2F124%2F68001

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