Defensive Strategies May Stabilize Unstable Competitive Systems: A Model of “Rock-Paper-Scissors-Lizard-Spock” in the Chemostat.

摘要

“Rock-paper-scissors” is a game played by two players to determine a single winner. In this paper, we state a continuous model of “rock-paper-scissors” in the chemostat and then generalize the model of “rock-paper-scissors” to a model of “rock-paper-scissors-lizard-Spock” in the chemostat that coincides with the biology of such relationships. The model we develop is based on a well-studied system of nonlinear differential equations that model these types of competitive relationships, which we then extend to give each organism a defense against its competitors in a “rockpaper- scissors-lizard-Spock” relationship. In a “rock-paper-scissors” relationship, it is rare to observe chaos/strange attractors. On the other hand, in a “rock-paper-scissors-lizard-Spock” relationship, chaos/strange attractors are typical. But, by giving a defense to a competitor, we numerically see that chaos/strange attractors can be eliminated from the system.