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Only noise can induce chaos in discrete populations
Author(s) -
Scheuring István,
Domokos Gábor
Publication year - 2007
Publication title -
oikos
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.672
H-Index - 179
eISSN - 1600-0706
pISSN - 0030-1299
DOI - 10.1111/j.2006.0030-1299.15287.x
Subject(s) - chaotic , statistical physics , noise (video) , range (aeronautics) , computer science , chaos (operating system) , state (computer science) , mathematics , algorithm , physics , artificial intelligence , image (mathematics) , computer security , materials science , composite material
Motivated by the papers from Ellner and Turchin 2005 and Dennis et al. 2003 we investigate the possibility to detect chaos in noisy ecological systems. One message of our paper is that if a dynamic model is available and if this model predicts chaotic behaviour, one should consider its discrete‐state, noisy version when fitting numerical predictions to observations. We emphasize that deterministic discrete‐state models behave periodically, thus only the interaction of these deterministic skeletons with random noise can produce non‐regular dynamics. We detect and describe a relatively sharply defined range of the noise (the grey zone) where the gradual transition from periodic to chaotic behaviour happens. This zone, the upper border of which can be predicted analytically, is identified in experimental data as well as in numerical simulations. In the grey zone the global, statistical behaviour will approach the statistics produced by the chaotic, continuous model, and in this sense we claim that noise can produce chaos.