Journal ArticleDOI
Chaotic Dynamics in an Insect Population
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TLDR
A nonlinear demographic model was used to predict the population dynamics of the flour beetle Tribolium under laboratory conditions and to establish the experimental protocol that would reveal chaotic behavior.Abstract:
A nonlinear demographic model was used to predict the population dynamics of the flour beetle Tribolium under laboratory conditions and to establish the experimental protocol that would reveal chaotic behavior. With the adult mortality rate experimentally set high, the dynamics of animal abundance changed from equilibrium to quasiperiodic cycles to chaos as adult-stage recruitment rates were experimentally manipulated. These transitions in dynamics corresponded to those predicted by the mathematical model. Phase-space graphs of the data together with the deterministic model attractors provide convincing evidence of transitions to chaos.read more
Citations
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A simple model for complex dynamical transitions in epidemics.
TL;DR: This work has shown that measles is a natural ecological system that exhibits different dynamical transitions at different times and places, yet all of these transitions can be predicted as bifurcations of a single nonlinear model.
Journal ArticleDOI
Noisy Clockwork: Time Series Analysis of Population Fluctuations in Animals
TL;DR: This work discusses recent advances in understanding ecological dynamics and testing theory using long-term data and reviews how dynamical forces interact to generate some central field and laboratory time series.
Journal ArticleDOI
Estimating community stability and ecological interactions from time‐series data
Anthony R. Ives,Anthony R. Ives,Brian Dennis,Brian Dennis,Kathryn L. Cottingham,Kathryn L. Cottingham,Stephen R. Carpenter,Stephen R. Carpenter +7 more
TL;DR: In this article, the authors derived three properties of stochastic multispecies communities that measure different characteristics associated with community stability using first-order multivariate autoregressive (MAR(1)) models.
Journal ArticleDOI
Fitting population models incorporating process noise and observation error
Perry de Valpine,Alan Hastings +1 more
TL;DR: The numerically integrated state-space (NISS) method as mentioned in this paper was proposed to fit models to time series of population abun- dances that incorporate both process noise and observation error in a likelihood framework.
Journal ArticleDOI
Chaos in a long-term experiment with a plankton community
Elisa Benincà,Jef Huisman,Reinhard Heerkloss,Klaus Jöhnk,Klaus Jöhnk,Pedro Branco,Egbert H. van Nes,Marten Scheffer,Stephen P. Ellner +8 more
TL;DR: The first experimental demonstration of chaos in a long-term experiment with a complex food web, isolated from the Baltic Sea, demonstrates that species interactions in food webs can generate chaos, and implies that stability is not required for the persistence of complex food webs, and that the long- term prediction of species abundances can be fundamentally impossible.
References
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Book
Non-linear time series. A dynamical system approach
TL;DR: Non-linear least-squares prediction based on non-linear models and case studies and an introduction to dynamical systems.
Journal ArticleDOI
Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos
TL;DR: This paper presents a dynamical regime in which (depending on the initial population value) cycles of any period, or even totally aperiodic but boundedpopulation fluctuations, can occur.
Journal ArticleDOI
Bifurcations and Dynamic Complexity in Simple Ecological Models
Robert M. May,George Oster +1 more
TL;DR: It is shown that as a hump steepens, the dynamics goes from a stable point, to a bifurcating hierarchy of stable cycles of period 2n, into a region of chaotic behavior where the population exhibits an apparently random sequence of "outbreaks" followed by "crashes".