Dresden 2006 – scientific programme
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AKB: Biologische Physik
AKB 17: Population Dynamics
AKB 17.4: Talk
Wednesday, March 29, 2006, 15:15–15:30, ZEU 260
Phase Transitions and Fluctuations in Stochastic Lattice Lotka-Volterra Models — •Mauro Mobilia1,2, Ivan T Georgiev2, and Uwe C Taeuber2 — 1Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München — 2Virginia Polytechnic Institute and State University, Blacksburg, USA
Modeling dynamics of interacting species has received considerable attention in the fields of biology and ecology since Lotka and Volterra’s pioneering work. In this contribution we report on the general properties of stochastic two-species competing populations with Lotka-Volterra type interactions defined on a d-dimensional lattice.
Introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical, deterministic mean-field picture. Already within mean-field theory, however, spatial constraints, modeling locally limited resources, lead to the emergence of a continuous phase transition. Field-theoretic arguments, supported by numerical results, indicate that this transition, which represents an extinction threshold for the predator population, is governed by the directed percolation universality class. In the active state, where predators and prey coexist, the classical center singularities with associated population cycles are replaced by either nodes or foci. In the vicinity of the stable nodes, the system is characterized by clusters of predators in a sea of prey. Near the stable foci, however, the stochastic lattice Lotka-Volterra system displays complex spatio-temporal patterns. We discuss the irregular oscillations of the population densities associated to spatial fluctuations and the robustness of the overall scenario.