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

Bashkirtseva, Irina; Chen, Guanrong; Ryashko, Lev

doi:10.1140/epjb/e2013-40592-2

Cited by 11 publications

(8 citation statements)

References 28 publications

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“…The value M = max m(t), t ∈ [0, T ] is a stochastic sensitivity factor of the cycle as a whole. Stochastic sensitivity function technique has been successfully applied to the analysis of 3D-cycles [Bashkirtseva et al, 2010], backward stochastic bifurcations [Bashkirtseva et al, 2013a], and for the solution of control problems [Bashkirtseva et al, 2012[Bashkirtseva et al, , 2013b.…”

Section: Appendixmentioning

confidence: 99%

Stochastic Bifurcations and Noise-Induced Chaos in a Dynamic Prey–Predator Plankton System

Bashkirtseva

Ryashko

2014

Int. J. Bifurcation Chaos

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We consider the stochastic Truscott-Brindley dynamical model of the interacting populations of prey and predator. We study a new phenomenon of the stochastic cycle splitting. In a zone of Canard cycles, using the stochastic sensitivity function technique, we find a critical value of the parameter corresponding to the supersensitive cycle. In the neighborhood of this critical value, a comparative parametrical analysis of the phenomenon of the stochastic cycle splitting is performed. It is shown that the bifurcation of the stochastic cycle splitting is accompanied by the noise-induced chaotization.

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Section: Appendixmentioning

confidence: 99%

Stochastic Bifurcations and Noise-Induced Chaos in a Dynamic Prey–Predator Plankton System

Bashkirtseva

Ryashko

2014

Int. J. Bifurcation Chaos

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“…So, the asymptotical approximations are the constructive alternative. Here, the quasipotential method [14] and the stochastic sensitivity function (SSF) technique [15,16,17] were successfully used for the solution of control problems [18,19].…”

Section: Introductionmentioning

confidence: 99%

Controlling stochastic sensitivity by the dynamic regulators

Bashkirtseva¹

2017

AIP Conference Proceedings

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Abstract.A problem of the control of stochastically forced equilibria in nonlinear dynamic systems with incomplete information is considered. Our approach is based on the idea of the synthesis of the required stochastic sensitivity for the equilibrium. We consider an important, from engineering point of view, case when the system states are observed partially, and these observations contain random noises. To solve this problem, a dynamic regulator consisting of the feedback and filter is constructed. Mathematically, the problem of the synthesis of the assigned stochastic sensitivity is reduced to the solution of the matrix equations for coefficients of the regulator. Problems of the controllability and attainability are discussed. The effectiveness of the proposed approach is demonstrated on the examples.

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“…In the framework of this approach, a stochastic sensitivity function (SSF) technique and geometrical description of stochastic attractors via confidence domains were proposed in [2,15]. SSF technique was successfully applied for the stabilization of stochastic attractors and suppression of chaos [3,19], and also for the analysis of noise-induced excitement in a prey-predator plankton system [20].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Sensitivity Analysis and Control for Ecological Model with the Allee Effect

Ryashko

Bashkirtseva

2015

Math. Model. Nat. Phenom.

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In this paper, we discuss a problem of the analysis and prevention of catastrophic shifts in ecosystems with stochastic environment. For the solution of this problem in models of ecological dynamics, a new approach based on the stochastic sensitivity functions technique is suggested and applied to a stochastically forced predator-prey model with the Allee effect. For this population model, we analyze a phenomenon of noise-induced extinction using the method of confidence domains. By controlling those domains we provide a stable coexistence of both species and prevent the noise-induced extinction.

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

Cited by 11 publications

References 28 publications

Stochastic Bifurcations and Noise-Induced Chaos in a Dynamic Prey–Predator Plankton System

Stochastic Bifurcations and Noise-Induced Chaos in a Dynamic Prey–Predator Plankton System

Controlling stochastic sensitivity by the dynamic regulators

Stochastic Sensitivity Analysis and Control for Ecological Model with the Allee Effect

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