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      Multistability in the cyclic competition system

      1 , 2 , 1
      Chaos: An Interdisciplinary Journal of Nonlinear Science
      AIP Publishing

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          Evolutionary games on graphs

          Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
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            The Importance of Being Discrete (and Spatial)

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              Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games

              Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non-hierarchical interactions among competing populations. Such non-transitive relations lead to an evolution with central features represented by the `rock-paper-scissors' game, where rock crushes scissors, scissors cut paper, and paper wraps rock. In combination with spatial dispersal of static populations, this type of competition results in the stable coexistence of all species and the long-term maintenance of biodiversity. However, population mobility is a central feature of real ecosystems: animals migrate, bacteria run and tumble. Here, we observe a critical influence of mobility on species diversity. When mobility exceeds a certain value, biodiversity is jeopardized and lost. In contrast, below this critical threshold all subpopulations coexist and an entanglement of travelling spiral waves forms in the course of temporal evolution. We establish that this phenomenon is robust, it does not depend on the details of cyclic competition or spatial environment. These findings have important implications for maintenance and evolution of ecological systems and are relevant for the formation and propagation of patterns in excitable media, such as chemical kinetics or epidemic outbreaks.
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                Author and article information

                Journal
                Chaos: An Interdisciplinary Journal of Nonlinear Science
                Chaos
                AIP Publishing
                1054-1500
                1089-7682
                November 2018
                November 2018
                : 28
                : 11
                : 113110
                Affiliations
                [1 ]Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
                [2 ]Department of Mathematics, KNU-Center for Nonlinear Dynamics, Kyungpook National University, Daegu 41566, Republic of Korea
                Article
                10.1063/1.5045366
                2c98f982-f38f-45cd-aa21-8394bfe3ac2e
                © 2018
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