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

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

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.

Suggested Citation

  • Tung, Wen-wen & Qi, Yan & Gao, J.B. & Cao, Yinhe & Billings, Lora, 2005. "Direct characterization of chaotic and stochastic dynamics in a population model with strong periodicity," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 645-652.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:2:p:645-652
    DOI: 10.1016/j.chaos.2004.09.076
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    Cited by:

    1. Bigdeli, N. & Afshar, K., 2009. "Characterization of Iran electricity market indices with pay-as-bid payment mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1577-1592.
    2. Çelik, C. & Merdan, H. & Duman, O. & Akın, Ö., 2008. "Allee effects on population dynamics with delay," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 65-74.
    3. Bigdeli, Nooshin & Haeri, Mohammad, 2009. "Time-series analysis of TCP/RED computer networks, an empirical study," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 784-800.
    4. Bigdeli, N. & Afshar, K., 2009. "Chaotic behavior of price in the power markets with pay-as-bid payment mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2560-2569.

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