title: Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model.
abstract: Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka-Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.
authors.affiliation: Instituto de Investigacion en Comunicacion Optica, Universidad Autonoma de San Luis Potosi, Karakorum 1470, Lomas 4a, 78220 San Luis Potosi, S.L.P., Mexico.
authors.forename: Valentin
authors.initials: V
authors.lastname: Afraimovich
authors.forename: Irma
authors.initials: I
authors.lastname: Tristan
authors.forename: Ramon
authors.initials: R
authors.lastname: Huerta
authors.forename: Mikhail I
authors.initials: MI
authors.lastname: Rabinovich
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D005716:Game Theory; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*; D012641:Selection, Genetic