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Sensitivity and chaos control for the forced nonlinear oscillations

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Barrio, R. & Borczyk, W. & Breiter, S., 2009. "Spurious structures in chaos indicators maps," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1697-1714.
    5. 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).
    6. 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.
    7. 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.
    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.

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