Seminars

Martin Luther King Day (No Seminar)

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Spring Break (No Seminar)

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Classes Begin (No Seminar)

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"Labor Day" (No Seminar)

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Spring Break (No Seminar)

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Dr. Jorge Puebla /b> RIKEN

Host:Prof. Satoru Emori

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Final Exams Week (No Seminar)

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Prof. Alastair Rucklidge

University of Leeds, Germany

"Cycling behavior and spatial structure in a hetero-clinic network model of Rock-Paper-Scissors-Spock-Lizard

The well-known game of Rock-Paper-Scissors can be used as a simple model of competition between three species. When modeled in continuous time using ordinary differential equations, the resulting system contains a hetero-clinic cycle between the three equilibrium solutions that represent the existence of only a single species. The game can be extended in asymmetric fashion by the addition of two further strategies (`Spock' and `Lizard'):now each strategy is dominant over two of the other four strategies, and is dominated by the remaining two. The ODE model contains coupled hetero-clinic cycles forming a hetero-clinic network. We develop a technique, based on the concept of fragmentary asymptotic stability, to understand the stability of arbitrarily long periodic sequences of visits made to the neighborhoods of the equilibrium. The regions of stability form a complicated pattern in parameter space. By adding spatial diffusion, we extend to a partial differential equation model and investigate the spatiotemporal evolution of these periodic itineraries.

Host: Prof. Uwe Tauber