Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos

Details Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos

Publishing date

Nov 1974

URL

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974sci...186..645m&link_type=abstract

Journals

Science, Volume 186, Issue 4164, pp. 645-647

Science

Mathematics

Field

Logic

Additional info 2

64

Type

Scientific paper

Abstract

Some of the simplest nonlinear difference equations describing the growth of biological populations with nonoverlapping generations can exhibit a remarkable spectrum of dynamical behavior, from stable equilibrium points, to stable cyclic oscillations between 2 population points, to stable cycles with 4, 8, 16,... points, through to a chaotic regime in which (depending on the initial population value) cycles of any period, or even totally aperiodic but bounded population fluctuations, can occur. This rich dynamical structure is overlooked in conventional linearized analyses; its existence in such fully deterministic nonlinear difference equations is a fact of considerable mathematical and ecological interest.

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