Sensitivity analysis of the stochastically and periodically forced Brusselator

Bashkirtseva, Irina; Ryashko, Lev

doi:10.1016/s0378-4371(99)00453-7

Cited by 56 publications

(33 citation statements)

References 13 publications

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“…Here, μ(t) > 0 is a T -periodic scalar stochastic sensitivity function satisfying the following boundary problem [28] with T -periodic coefficients a(t) = p (t)(F (t) + F (t))p(t), b(t) = p (t)S(t)p(t),…”

Section: Appendix: Background and The Ssf Techniquementioning

confidence: 99%

Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach

2013

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Abstract. In this paper, noise-induced destruction of self-sustained oscillations is studied for a stochastically-forced generator with hard excitement. The problem is to design a feedback regulator that can stabilize a limit cycle of the closed-loop system and to provide a required dispersion of the generated oscillations. The approach is based on the stochastic sensitivity function (SSF) technique and confidence domain method. A theory about the synthesis of assigned SSF is developed. For the case when this control problem is ill-posed, a regularization method is constructed. The effectiveness of the new method of confidence domain is demonstrated by stabilizing auto-oscillations in a randomly-forced generator with hard excitement.

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Section: Appendix: Background and The Ssf Techniquementioning

confidence: 99%

Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach

2013

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“…Here, m(t) > 0 is a T -periodic scalar stochastic sensitivity function satisfying the following boundary problem [8] …”

Section: Stochastic Sensitivity Function Technique Consider a Nonlinearmentioning

confidence: 99%

Stochastic sensitivity and noise-induced bifurcations of limit cycles

Ryashko¹

2013

ams

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“…Благодаря высокой чувстви-тельности аттракторов в зонах бифуркаций даже весьма малые шумы могут порождать качественные изменения динамики. Анализ стохастической чувствительности аттракторов нелинейных систем, находящихся под воздействием случайных возмущений, позволяет ве-сти конструктивное исследование подобных изменений [13,14].…”

Section: § 1 введениеunclassified

“…Техника ФСЧ была введена ранее в ра-ботах [13,29,30,31], где с ее помощью исследовались стохастические циклы нелинейных систем с непрерывным временем. Конструктивные возможности данного подхода продемон-стрированы в [31] для задачи возбуждения и подавления хаоса и в [32] для задачи анализа индуцированных шумом переходов между периодическими аттракторами стохастической системы Лоренца.…”

Section: § 1 введениеunclassified

Backward stochastic bifurcations of the discrete system cycles

Bashkirtseva¹,

Ryashko²,

Fedotov³

et al. 2010

Nelin. Dinam.

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В работе рассматриваются стохастически возмущенные предельные циклы дискретных динамических систем в зоне удвоения периода. Исследуется явление обратных стохастиче-ских бифуркаций (ОСБ) -уменьшения кратности цикла при увеличении интенсивности шума. Предлагается метод анализа ОСБ на основе техники функции стохастической чув-ствительности. Конструктивные возможности данного метода демонстрируются на примере анализа ОСБ стохастических циклов систем Ферхюльста и Риккера.Ключевые слова: бифуркации, дискретные системы, модель Ферхюльста, стохастиче-ская чувствительность I. A. Bashkirtseva, L. B. Ryashko, S. P. Fedotov, I. N. Tsvetkov Backward stochastic bifurcations of the discrete system cycles We study stochastically forced limit cycles of discrete dynamical systems in a perioddoubling bifurcation zone. A phenomenon of a decreasing of the stochastic cycle multiplicity with a noise intensity growth is investigated. We call it by a backward stochastic bifurcation (BSB). In this paper, for the BSB analysis we suggest a stochastic sensitivity function technique. As a result, a method for the estimation of critical values of noise intensity corresponding to BSB is proposed. The constructive possibilities of this general method for the detailed BSB analysis of the multiple stochastic cycles of the forced Verhulst and Ricker systems are demonstrated.

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Sensitivity analysis of the stochastically and periodically forced Brusselator

Cited by 56 publications

References 13 publications

Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach

Stabilizing stochastically-forced oscillation generators with hard excitement: a confidence-domain control approach

Stochastic sensitivity and noise-induced bifurcations of limit cycles

Backward stochastic bifurcations of the discrete system cycles

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