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Stochastic sensitivity of 3D-cycles

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  • Bashkirtseva, I.A.
  • Ryashko, L.B.

Abstract

The limit cycles of nonlinear systems under the small stochastic disturbances are considered. The random trajectories of forced system leave the deterministic cycle and form some stochastic bundle around it. The probabilistic description of this bundle near cycle based on stochastic sensitivity function (SSF) is suggested. The SSF is a covariance matrix for periodic solution of linear stochastic first approximation system. This matrix is a solution of the boundary problem for linear matrix differential equation. For 3D-cycles this matrix differential equation on the basis of singular expansion is reduced to the system of three scalar equations only. The possibilities of SSF to describe some peculiarities of stochastically forced Roessler model are demonstrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:66:y:2004:i:1:p:55-67
    DOI: 10.1016/j.matcom.2004.02.021
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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.
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    Cited by:

    1. 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).
    2. 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).
    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. 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.
    5. Bashkirtseva, Irina & Ryashko, Lev, 2005. "Sensitivity and chaos control for the forced nonlinear oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1437-1451.
    6. 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.
    7. 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.
    8. Yihan Wang & Jinjie Zhu, 2023. "Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation," Mathematics, MDPI, vol. 11(11), pages 1-10, June.
    9. 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).
    10. 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).
    11. 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).
    12. 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.

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