IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v186y2024ics0960077924007987.html
   My bibliography  Save this article

Routes to chaos and bistability in the Rypdal model with a parametric disturbance

Author

Listed:
  • Alvarez, Arnold A.
  • Brugnago, Eduardo L.
  • Caldas, I.L.

Abstract

In this work, we propose a parametric perturbation in the plasma production rate of the Rypdal model. This low-dimensional Lorenz-like system is derived from a two-field model for transport in Helimak magnetically confined plasmas. We analyze the stability of the equilibrium points and study the emergence of chaos in the disturbed system. As a perturbation result, the attractor structure is modified, and shrimp-shaped domains occur in the parameter plane, where there are periodic spirals immersed in the chaotic region, both behaviors characterized by the largest Lyapunov exponent. Along these periodic domains, we identify the bistability of attractors, period-doubling cascades, and a route to chaos via bifurcations and collisions of periodic orbits. By the isospikes per period, we schematize the hierarchical organization of periodic attractors into the shrimp spirals.

Suggested Citation

  • Alvarez, Arnold A. & Brugnago, Eduardo L. & Caldas, I.L., 2024. "Routes to chaos and bistability in the Rypdal model with a parametric disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007987
    DOI: 10.1016/j.chaos.2024.115246
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924007987
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115246?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Reis, A.S. & Brugnago, E.L. & Viana, R.L. & Batista, A.M. & Iarosz, K.C. & Ferrari, F.A.S. & Caldas, I.L., 2023. "The role of the fitness model in the suppression of neuronal synchronous behavior with three-stage switching control in clustered networks," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Medeiros, E.S. & de Souza, S.L.T. & Medrano-T, R.O. & Caldas, I.L., 2011. "Replicate periodic windows in the parameter space of driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 982-989.
    3. Brugnago, Eduardo L. & da Silva, Rafael M. & Manchein, Cesar & Beims, Marcus W., 2020. "How relevant is the decision of containment measures against COVID-19 applied ahead of time?," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Klapcsik, Kálmán & Hegedűs, Ferenc, 2017. "The effect of high viscosity on the evolution of the bifurcation set of a periodically excited gas bubble," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 198-208.
    2. James, Nick & Menzies, Max, 2023. "Collective infectivity of the pandemic over time and association with vaccine coverage and economic development," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Trobia, José & de Souza, Silvio L.T. & dos Santos, Margarete A. & Szezech, José D. & Batista, Antonio M. & Borges, Rafael R. & Pereira, Leandro da S. & Protachevicz, Paulo R. & Caldas, Iberê L. & Iaro, 2022. "On the dynamical behaviour of a glucose-insulin model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Alberto Olivares & Ernesto Staffetti, 2021. "Optimal Control Applied to Vaccination and Testing Policies for COVID-19," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    5. Olivares, Alberto & Staffetti, Ernesto, 2021. "Uncertainty quantification of a mathematical model of COVID-19 transmission dynamics with mass vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Sharov, Konstantin S., 2020. "Creating and applying SIR modified compartmental model for calculation of COVID-19 lockdown efficiency," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    7. da Costa, Diogo Ricardo & Hansen, Matheus & Batista, Antonio Marcos, 2019. "Parametric perturbation in a model that describes the neuronal membrane potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 519-525.
    8. Varga, Roxána & Klapcsik, Kálmán & Hegedűs, Ferenc, 2020. "Route to shrimps: Dissipation driven formation of shrimp-shaped domains," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    9. Olivares, Alberto & Staffetti, Ernesto, 2023. "A statistical moment-based spectral approach to the chance-constrained stochastic optimal control of epidemic models," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    10. da Costa, Diogo Ricardo & Rocha, Julia G.S. & de Paiva, Luam S. & Medrano-T, Rene O., 2021. "Logistic-like and Gauss coupled maps: The born of period-adding cascades," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    11. de Souza, Silvio L.T. & Batista, Antonio M. & Caldas, Iberê L. & Iarosz, Kelly C. & Szezech Jr, José D., 2021. "Dynamics of epidemics: Impact of easing restrictions and control of infection spread," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007987. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.