Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity

Wen Wen Tung, Yan Qi, J. B. Gao, Yinhe Cao, Lora Billings

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In recent years it has been increasingly recognized that noise and determinism may have comparable but different influences on population dynamics. However, no simple analysis methods have been introduced into ecology which can readily characterize those impacts. In this paper, we study a population model with strong periodicity and both with and without noise. The noise-free model generates both quasi-periodic and chaotic dynamics for certain parameter values. Due to the strong periodicity, however, the generated chaotic dynamics have not been satisfactorily described. The dynamics becomes even more complicated when there is noise. Characterizing the chaotic and stochastic dynamics in this model thus represents a challenging problem. Here we show how the chaotic dynamics can be readily characterized by the direct dynamical test for deterministic chaos developed by [Gao JB, Zheng ZM. Europhys. Lett. 1994;25:485] and how the influence of noise on quasi-periodic motions can be characterized as asymmetric diffusions wandering along the quasi-periodic orbit. It is hoped that the introduced methods will be useful in studying other population models as well as population time series obtained both in field and laboratory experiments.

Original languageEnglish
Pages (from-to)645-652
Number of pages8
JournalChaos, Solitons and Fractals
Volume24
Issue number2
DOIs
StatePublished - 1 Apr 2005

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Stochastic Dynamics
Chaotic Dynamics
Population Model
Periodicity
Quasi-periodic Motion
Deterministic Chaos
Determinism
Ecology
Population Dynamics
Periodic Orbits
Time series
Model
Experiment
Influence

Cite this

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title = "Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity",
abstract = "In recent years it has been increasingly recognized that noise and determinism may have comparable but different influences on population dynamics. However, no simple analysis methods have been introduced into ecology which can readily characterize those impacts. In this paper, we study a population model with strong periodicity and both with and without noise. The noise-free model generates both quasi-periodic and chaotic dynamics for certain parameter values. Due to the strong periodicity, however, the generated chaotic dynamics have not been satisfactorily described. The dynamics becomes even more complicated when there is noise. Characterizing the chaotic and stochastic dynamics in this model thus represents a challenging problem. Here we show how the chaotic dynamics can be readily characterized by the direct dynamical test for deterministic chaos developed by [Gao JB, Zheng ZM. Europhys. Lett. 1994;25:485] and how the influence of noise on quasi-periodic motions can be characterized as asymmetric diffusions wandering along the quasi-periodic orbit. It is hoped that the introduced methods will be useful in studying other population models as well as population time series obtained both in field and laboratory experiments.",
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Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity. / Tung, Wen Wen; Qi, Yan; Gao, J. B.; Cao, Yinhe; Billings, Lora.

In: Chaos, Solitons and Fractals, Vol. 24, No. 2, 01.04.2005, p. 645-652.

Research output: Contribution to journalArticle

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