Regensburg 2019 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 10: Evolutionary Game Theory (joint SOE/BP/DY) (joint session SOE/BP)

SOE 10.2: Talk

Tuesday, April 2, 2019, 12:00–12:30, H17

Control of biodiversity in evolutionary dynamics: extension to higher dimensions — •Jens Christian Claussen — Department of Mathematics, Aston University, Birmingham B4 7ET, U.K.

Cyclic dominance, as observed in biology and socio-economic systems, has frequently been investigated in its role towards stabilization of diversity of strategies [PRL 100, 058104], and it has been shown that the introduction of a parameter in the payoff matrix can lead to a stabilization of the symmetric state of coexistence. Recently, we had introduced a feedback control method which utilizes a feedback term derived from a conserved property of motion of the case of a neutral oscillation. This mechanism was discussed, analyzed and numerically demonstrated explicitly for the cyclic rock-paper-scissors game. Here, we discuss the generalization to cyclic dominance of M strategies and their implications. First, it is observed that the straightforward generalization leads again to payoff functions with polynomial degrees up to third order, multiplied by the feedback term which in this case is of order M, resulting in characteristic polynomials of order 2(M + 2), compared to order 4 without control, prohibiting closed eigenvalue expressions even for the fixed point stability. To circumvent this, alternative feedback functions are introduced which allow for lower orders. Finally, we discuss the applicability of this approach.