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Spiral periodic structures in a parameter plane of an ecological model

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  • da Silva, Rodrigo A.
  • Rech, Paulo C.

Abstract

We investigate a parameter plane of a set of three autonomous, ten-parameter, first-order nonlinear ordinary differential equations, which models a tri-trophic food web system. By using Lyapunov exponents, bifurcation diagrams, and trajectories in the phase-space, to numerically characterize the dynamics of the model in a parameter plane, we show that it presents typical periodic structures embedded in a chaotic region, forming a spiral structure that coils up around a focal point while period-adding bifurcations take place.

Suggested Citation

  • da Silva, Rodrigo A. & Rech, Paulo C., 2015. "Spiral periodic structures in a parameter plane of an ecological model," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 9-13.
    • Handle: RePEc:eee:apmaco:v:254:y:2015:i:c:p:9-13
    DOI: 10.1016/j.amc.2014.12.115
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    References listed on IDEAS

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    1. Cabeza, Cecilia & Briozzo, Carlos A. & Garcia, Rodrigo & Freire, Joana G. & Marti, Arturo C. & Gallas, Jason A.C., 2013. "Periodicity hubs and wide spirals in a two-component autonomous electronic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 59-65.
    2. Freire, Joana G. & Gallas, Jason A.C., 2014. "Cyclic organization of stable periodic and chaotic pulsations in Hartley’s oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 129-134.
    3. Fabiola Prants & Paulo Rech, 2014. "Organization of periodic structures in a damped-forced oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(9), pages 1-4, September.
    4. Giorgio E. Testoni & Paulo C. Rech, 2010. "Dynamics Of A Particular Lorenz Type System," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 973-982.
    5. Paulo Rech, 2013. "Nonlinear dynamics investigation in parameter planes of a periodically forced compound KdV-Burgers equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(8), pages 1-5, August.
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    Cited by:

    1. da Silva, Angela & Rech, Paulo C., 2018. "Numerical investigation concerning the dynamics in parameter planes of the Ehrhard–Müller system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 152-157.
    2. Hossain, Mainul & Kumbhakar, Ruma & Pal, Nikhil, 2022. "Dynamics in the biparametric spaces of a three-species food chain model with vigilance," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Borghezan, Monik & Rech, Paulo C., 2017. "Chaos and periodicity in Vallis model for El Niño," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 15-18.

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