67 results found
Reichenbach T, Frey E, Franosch T, 2007, Traffic jams induced by rare switching events in two-lane transport, NEW JOURNAL OF PHYSICS, Vol: 9, ISSN: 1367-2630
Reichenbach T, Mobilia M, Frey E, 2006, Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol: 74, ISSN: 1539-3755
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see, e.g., B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature 418, 171 (2002)] and B. Kirkup and M. A. Riley [Nature 428, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely, the â€œrock-paper- scissorsâ€ or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems. © 2006 The American Physical Society.
Reichenbach T, Mobilia M, Frey E, 2006, Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model, PHYSICAL REVIEW E, Vol: 74, ISSN: 2470-0045
Reichenbach T, Franosch T, Frey E, 2006, Exclusion processes with internal states, PHYSICAL REVIEW LETTERS, Vol: 97, ISSN: 0031-9007
Reichenbach T, 2005, Retarded functions in noncommutative theories, PHYSICS LETTERS B, Vol: 612, Pages: 275-282, ISSN: 0370-2693
Reichenbach T, 2005, Retarded functions in noncommutative theories, Physics Letters B, Vol: 612, Pages: 275-282, ISSN: 0370-2693
Reichenbach T, 2005, Violation of remaining Lorentz symmetry in the approach of time-ordered perturbation theory to space-time noncommutativity, PHYSICS LETTERS B, Vol: 606, Pages: 403-407, ISSN: 0370-2693
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