Emergence of first-order and second-order phase transitions in a cyclic ecosystem exposed to environmental impact

A cyclically dominating three-species ecosystem, modeled within the framework of rock-paper-scissor game, is studied in presence of natural death and an effect of the environment. The environmental impact is parameterized along with the death rates in the rate equation of the species densities. Monte-Carlo simulations on this system reveal that the population density bears the signature of first-order and second-order phase transitions in different regimes of the parameters representing natural deaths of the species. The connection of this phenomena with the phase transitions is also supported by the behavior of the basin entropy calculated for the system. The density of total population evidently becomes an order parameter with respect to the change in environmental impact on the system.