Regensburg 2016 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Poster - Complex nonlinear systems

DY 30.10: Poster

Dienstag, 8. März 2016, 18:15–21:00, Poster C

Feedback control in evolutionary dynamics: controlling the coexistence state — •Jens Christian Claussen — Computational Systems Biology, Jacobs University Bremen

Evolutionary dynamics in the frameworks of Lotka-Volterra systems and replicator equations in evolutionary game theory can include fixed points and cycles which can be neutrally stable, repelling or attracting. Of particular interest is the case where a coexistence state loses stability due to non-zero-sum payoffs, corresponding to dissipative interactions. Here I introduce a general ansatz of feedback control where an additive control term is implemented in the payoff matrix which is chosen proportional to an observable of the system which is suitably chosen to reflect the distance from the fixed point. This feedback control is implemented for the Rock-Paper-Scissors system which has applications in biology and in socio-economic systems, and for which the loss of stability depending on payoffs and population size has been recently discussed [J. Claussen and A. Traulsen, PRL 100, 058104 (2008)]. As the discretization stochasticity in a finite population additionally destabilizes coexistence, here I discuss also an implementation by a pairwise comparison process to demonstrate that the control scheme is applicable in a finite population.