Dresden 2014 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 10: Nonlinear Stochastic Systems
DY 10.1: Talk
Tuesday, April 1, 2014, 09:30–09:45, ZEU 160
Fluctuation-Driven Shifts in Selection Regimes in Population Dynamics — •Yen Ting Lin1, Hyejin Kim2, and Charles Doering3 — 1Max Planck Institutes for the Physics of Complex Systems, Noetnitzer Str. 38, Dresden 01187 , Germany — 2Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA — 3Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
Demographic stochasticity is an essential feature of population dynamics. Nevertheless theoretical investigations often neglect this naturally occurring noise due to the mathematical complexity of stochastic models. This talk reports the results of analytical and computational investigations of models of competitive population dynamics, specifically the competition between species in heterogeneous environments with different phenotypes of dispersal, fully accounting for demographic stochasticity. A novel asymptotic approximation is introduced and applied to derive remarkably simple analytical forms for key statistical quantities describing the populations' dynamical evolution. The theory is verified by conventional asymptotic analysis and large-scale numerical simulations. Both dynamical mechanisms and time scales of the fluctuation-induced phenomena are identified within the theoretical approach. The analysis highlights the fundamental physical effect of the fluctuations and provides an intuitive interpretation of the complex dynamics. An interaction between stochasticity and nonlinearity is the foundation of noise-driven dynamical selection.