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Switching induced oscillations in discrete one-dimensional systems

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  • Mendoza, Steve A.
  • Peacock-López, Enrique

Abstract

In ecological modeling, seasonality can be represented as an alternation between environmental conditions. We consider a switching strategy that alternates between two undesirable dynamics and find that they can yield a desirable periodic behavior in the case of the Beverton–Holt, Ricker, and modified Ricker maps, which have been extensively used to model ecological populations. For the Ricker and modified Ricker models, we observe coexistence of attractors, which, under the same conditions, define basin of attractions, and the final dynamic behavior depends on the initial conditions.

Suggested Citation

  • Mendoza, Steve A. & Peacock-López, Enrique, 2018. "Switching induced oscillations in discrete one-dimensional systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 35-44.
    • Handle: RePEc:eee:chsofr:v:115:y:2018:i:c:p:35-44
    DOI: 10.1016/j.chaos.2018.08.001
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    References listed on IDEAS

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    1. Silva, Emily & Peacock-Lopez, Enrique, 2017. "Seasonality and the logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 152-156.
    2. Amengual, P. & Meurs, P. & Cleuren, B. & Toral, R., 2006. "Reversals of chance in paradoxical games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 641-648.
    3. Mendoza, Steve A. & Matt, Eliza W. & Guimarães-Blandón, Diego R. & Peacock-López, Enrique, 2018. "Parrondo’s paradox or chaos control in discrete two-dimensional dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 86-93.
    4. Levinsohn, Erik A. & Mendoza, Steve A. & Peacock-López, Enrique, 2012. "Switching induced complex dynamics in an extended logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 426-432.
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    Cited by:

    1. Cánovas, Jose S. & Rezgui, Houssem Eddine, 2023. "Revisiting the dynamic of q-deformed logistic maps," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Lai, Joel Weijia & Cheong, Kang Hao, 2022. "Risk-taking in social Parrondo’s games can lead to Simpson’s paradox," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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