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Uwe Tauber
Dept. of Physics & Ctr. for Stochastic Processes in Science & Engineering
Virginia Polytechnic Institute and State University

The Role of Stochastic Fluctations and Spatio-Temporal Correlations in Lattice Models for Predator-Prey Interactions

We have studied different variants of two-species predator-prey models defined on a lattice. Introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidate the classical Lotka-Volterra mean-field picture. Moreover, site occupation constraints, modeling locally limited resources, lead to the emergence of either a continuous active-to-absorbing state transition or to a first-order phase transition. In the former case, the universal critical peoperties near the extinction threshold are governed by the directed percolation universality class. In the active state, where predators and prey coexist, the classical limit cycles or centers are replaced by either nodes or foci, and the system displays complex and correlated spatio-temporal patterns of competing fronts of activity. Finite systems near stable foci are characterized by irregular population number oscillations, whose features are determined by the intrinsic interaction rates rather than initial conditions. In the thermodynamic limit, however, the densities of predators and prey exhibit damped oscillatory behavior. We illustrate these general issues by considering in detail ecologically motivated models with nearest-neighbor interactions, as well as other variants with nearest and next-nearest neighbor interactions.

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