Blowing-up of deterministic fixed points in stochastic population dynamics.

NATIELLO, MA; HERNAN GUSTAVO SOLARI

MATHEMATICAL BIOSCIENCES

ELSEVIER SCIENCE INC

Año: 2007 vol. 209 p. 319 - 335

0025-5564

    We discuss the stochastic dynamics of biological (and other) popula-tions presenting a limit behaviour for large environments (called determin-istic limit) and its relation with the dynamics in the limit. The discussionis circumscribed to linearly stable fixed points of the deterministic dy-namics, and it is shown that the cases of extinction and non-extinctionequilibriums present different features. Mainly, non-extinction equilibriahave associated a region of stochastic instability surrounded by a regionof stochastic stability. The instability region does not exist in the case ofextinction fixed points, and a linear Lyapunov function can be associatedwith them. Stochastically sustained oscillations of two subpopulations arealso discussed in the case of complex eigenvalues of the stability matrixof the deterministic system.