Attractors of randomly forced logistic model with delay: stochastic sensitivity and noise-induced transitions

Bashkirtseva, Irina; Ekaterinchuk, Ekaterina; Ryashko, Lev

doi:10.1080/10236198.2015.1100610

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…The results of this section are illustrated for a point equilibrium in Example III. 3, where even local stabilization is not possible for any α ∈ (0, 1) in the absence of a stochastic perturbation, and in Example III. 5, where global stabilization is considered.…”

Section: B Predictive Based Controlmentioning

confidence: 99%

“…For both differential and difference equations, more detailed historical notes, as well as recent results on the topic are given in 7,9,20 . Recently, stability and stabilization of stochastic difference equations and systems, as well as cyclic and chaotic behaviour, has become a focus of many publications 2,3,12,18,21,27,30,33 . Moreover, a developed theory of random difference equations was utilized to investigate differential equations 11 , or discrete and continuous stochastic equations were considered in the framework of a single model 14 .…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of cycles with stochastic prediction-based and target-oriented control

Braverman

Kelly

Rodkina

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We stabilize a prescribed cycle or an equilibrium of a difference equation using pulsed stochastic control. Our technique, inspired by Kolmogorov's Law of Large Numbers, activates a stabilizing effect of stochastic perturbation and allows for stabilization using a much wider range for the control parameter than would be possible in the absence of noise. Our main general result applies to both Prediction-Based and Target-Oriented Controls. This analysis is the first to make use of the stabilizing effects of noise for Prediction-Based Control; the stochastic version has previously been examined in the literature, but only the destabilizing effect of noise was demonstrated. A stochastic variant of Target-Oriented Control has never been considered, to the best of our knowledge, and we propose a specific form that uses a point equilibrium or one point on a cycle as a target. We illustrate our results numerically on the logistic, Ricker and Maynard Smith models from population biology.

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Section: B Predictive Based Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stabilization of cycles with stochastic prediction-based and target-oriented control

Braverman

Kelly

Rodkina

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…To analyse the noise-induced extinction one can use the stochastic sensitivity function technique [16,21,22]. In Figure 11, confidence ellipses constructed on the base of the stochastic sensitivity function technique are plotted for β = 0.73 and ε = 0.01 (green), ε = 0.1 (red).…”

Section: -6mentioning

confidence: 99%

Noise-induced shifts in the ecological model with delay

Ryashko

Tsvetkov

Spagnolo

2019

Proceedings of the 45th International Conference on Application of Mathematics in Engineering and Economics (Amee’19)

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A Hassell-type mathematical model of population dynamics with delay and stochastic disturbances is considered. In this bistable model, one of the attractors corresponds to the extinction, and the other one describes non-trivial stable modes of dynamics. These modes can be both regular and chaotic. Structural stability zones are separated by local and global bifurcations. We study how noise shifts these bifurcation points and contracts the persistence zone. Abilities of the theoretical analysis of these phenomena with the help of the stochastic sensitivity function technique is discussed.

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“…With a further increase in μ, the closed invariant curve expands, becomes non-smooth, and collapses before being transformed into the discrete cycle. For β = 0.51, a variety of attractors and bifurcations is the same as for the β = 1 case considered in detail in [8].…”

Section: Deterministic Modelmentioning

confidence: 99%

Analysis of noise-induced transitions in a generalized logistic model with delay near Neimark–Sacker bifurcation

Bashkirtseva¹,

Ekaterinchuk²,

Ryashko³

2017

J. Phys. A: Math. Theor.

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We consider an effect of random disturbances on the generalized logistic model with delay in mono- and bistable regimes near Neimark–Sacker bifurcation. Noise-induced transitions between coexisting attractors, and between separate parts of the unique attractor, are studied. We suggest a semi-analytical approach that combines a geometric analysis of the mutual arrangement of attractors, their basins of attraction, and corresponding confidence domains found by the stochastic sensitivity functions technique. Constructive abilities of this approach are demonstrated for the generalized logistic model with delay.

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Attractors of randomly forced logistic model with delay: stochastic sensitivity and noise-induced transitions

Cited by 6 publications

References 19 publications

Stabilization of cycles with stochastic prediction-based and target-oriented control

Stabilization of cycles with stochastic prediction-based and target-oriented control

Noise-induced shifts in the ecological model with delay

Analysis of noise-induced transitions in a generalized logistic model with delay near Neimark–Sacker bifurcation

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