IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v26y2005i5p1437-1451.html
   My bibliography  Save this article

Sensitivity and chaos control for the forced nonlinear oscillations

Author

Listed:
  • Bashkirtseva, Irina
  • Ryashko, Lev

Abstract

This paper is devoted to study the problem of controlling chaos for forced nonlinear dynamic systems. We suggest a new control technique based on sensitivity analysis. With the help of approximation of nonequilibrium quasipotential, stochastic sensitivity function (SSF) is constructed. This function is used as basic tool of a quantitative description for a system response on the random external disturbances. The possibilities of SSF to predict chaotic dynamics for the periodic and stochastic forced Brusselator are shown. The problem of chaos control based on SSF is considered. A design of attractors with the desired features by feedback regulator is discussed. Analysis of controllability and effective technique for regulator synthesis is presented. An example of suppressing chaos for Brusselator is considered.

Suggested Citation

  • Bashkirtseva, Irina & Ryashko, Lev, 2005. "Sensitivity and chaos control for the forced nonlinear oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1437-1451.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1437-1451
    DOI: 10.1016/j.chaos.2005.03.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905003073
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.03.029?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. Bashkirtseva, I.A & Ryashko, L.B, 2000. "Sensitivity analysis of the stochastically and periodically forced Brusselator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 126-139.
    2. Fedotov, Sergei & Bashkirtseva, Irina & Ryashko, Lev, 2004. "Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 491-506.
    3. Bashkirtseva, I.A. & Ryashko, L.B., 2004. "Stochastic sensitivity of 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(1), pages 55-67.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barrio, R. & Borczyk, W. & Breiter, S., 2009. "Spurious structures in chaos indicators maps," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1697-1714.
    2. Irina Bashkirtseva & Alexander Pisarchik & Lev Ryashko & Tatyana Ryazanova, 2016. "Excitability And Complex Mixed-Mode Oscillations In Stochastic Business Cycle Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(01n02), pages 1-16, February.
    3. Bashkirtseva, Irina & Ryashko, Lev & Schurz, Henri, 2009. "Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 72-82.
    4. Goharrizi, Amin Yazdanpanah & Khaki-Sedigh, Ali & Sepehri, Nariman, 2009. "Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2448-2455.
    5. Ryashko, L. & Bashkirtseva, I. & Gubkin, A. & Stikhin, P., 2009. "Confidence tori in the analysis of stochastic 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 256-269.
    6. Slepukhina, E. & Ryashko, L. & Kügler, P., 2020. "Noise-induced early afterdepolarizations in a three-dimensional cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    7. Jochen Jungeilges & Tatyana Ryazanova, 2018. "Output volatility and savings in a stochastic Goodwin economy," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 8(3), pages 355-380, December.
    8. Irina Bashkirtseva & Makar Pavletsov & Tatyana Perevalova & Lev Ryashko, 2023. "Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger," Mathematics, MDPI, vol. 11(20), pages 1-14, October.
    9. Bashkirtseva, Irina & Ryazanova, Tatyana & Ryashko, Lev, 2015. "Analysis of dynamic regimes in stochastically forced Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 96-104.

    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. Ryashko, L. & Bashkirtseva, I. & Gubkin, A. & Stikhin, P., 2009. "Confidence tori in the analysis of stochastic 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 256-269.
    2. Irina Bashkirtseva & Davide Radi & Lev Ryashko & Tatyana Ryazanova, 2018. "On the Stochastic Sensitivity and Noise-Induced Transitions of a Kaldor-Type Business Cycle Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 699-718, March.
    3. Mandal, Partha Sarathi, 2018. "Noise-induced extinction for a ratio-dependent predator–prey model with strong Allee effect in prey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 40-52.
    4. Bashkirtseva, Irina & Ryashko, Lev, 2017. "Stochastic sensitivity analysis of noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 573-584.
    5. Bashkirtseva, Irina & Ryashko, Lev & Schurz, Henri, 2009. "Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 72-82.
    6. Bashkirtseva, I.A. & Ryashko, L.B., 2004. "Stochastic sensitivity of 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(1), pages 55-67.
    7. Irina Bashkirtseva & Makar Pavletsov & Tatyana Perevalova & Lev Ryashko, 2023. "Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger," Mathematics, MDPI, vol. 11(20), pages 1-14, October.
    8. Bashkirtseva, Irina & Ryashko, Lev, 2013. "Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 295-306.
    9. Slepukhina, Evdokiia & Bashkirtseva, Irina & Ryashko, Lev & Kügler, Philipp, 2022. "Stochastic mixed-mode oscillations in the canards region of a cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Bashkirtseva, I. & Ryashko, L., 2020. "Analysis of noise-induced phenomena in the nonlinear tumor–immune system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    11. Bashkirtseva, Irina & Perevalova, Tatyana & Ryashko, Lev, 2020. "Noise-induced shifts in dynamics of multi-rhythmic population SIP-model," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    12. Slepukhina, E. & Ryashko, L. & Kügler, P., 2020. "Noise-induced early afterdepolarizations in a three-dimensional cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    13. Kelly, Cónall, 2016. "Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 480-491.
    14. Slepukhina, Evdokia & Bashkirtseva, Irina & Ryashko, Lev, 2020. "Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    15. Yihan Wang & Jinjie Zhu, 2023. "Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation," Mathematics, MDPI, vol. 11(11), pages 1-10, June.
    16. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2020. "Analysis of regular and chaotic dynamics in a stochastic eco-epidemiological model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

    More about this item

    Statistics

    Access and download statistics

    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:26:y:2005:i:5:p:1437-1451. 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.