Models of the population playing the rock-paper-scissors game

Włodzimierz Bąk; Tadeusz Nadzieja; Mateusz Wróbel

doi:10.3934/dcdsb.2018001

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2018, Volume 23, Issue 1: 1-11. Doi: 10.3934/dcdsb.2018001

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Models of the population playing the rock-paper-scissors game

Instytut Matematyki i Informatyki, Uniwersytet Opolski, ul. Oleska 48, Poland

Received: September 30, 2016

Revised: January 31, 2017

Published: November 2017

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Abstract

We consider discrete dynamical systems coming from the models of evolution of populations playing rock-paper-scissors game. Asymptotic behaviour of trajectories of these systems is described, occurrence of the Neimark-Sacker bifurcation and nonexistence of time averages are proved.

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Mathematics Subject Classification: Primary: 37C05, 91A05.

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Figure 1. Levels of Lyapunov function.

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Figure 2. Sample trajectories of $V_{\lambda}$.

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