Transitions between metastable states in a simplified model for the thermohaline circulation under random fluctuations

Tesfay, Daniel; Wei, Pingyuan; Zheng, Yayun; Duan, Jinqiao; Kurths, Jürgen

doi:10.1016/j.amc.2019.124868

Cited by 11 publications

(8 citation statements)

References 22 publications

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“…Subsequently, Zheng et al [38] developed a probabilistic framework to investigate the maximum likelihood climate change for an energy balance system under the combined influence of greenhouse effect and α-stable Lévy motions. Additionally, there are also some researchers using the Lévy motion to characterize the random fluctuations emerged in neural systems [28], gene networks [6], epidemic model [21], and the Earth systems [2,20,33,34,37].…”

Section: Mathematics Subject Classification (2020) Msc 60g51 • Msc 60...mentioning

confidence: 99%

Extracting stochastic dynamical systems with $α$-stable Lévy noise from data

Li,

Lu,

et al. 2021

Preprint

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With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extract stochastic dynamical systems with (non-Gaussian) Lévy noise are relatively few so far. In this work, we propose a data-driven method to extract stochastic dynamical systems with α-stable Lévy noise from short burst data based on the properties of α-stable distributions. More specifically, we first estimate the Lévy jump measure and noise intensity via computing mean and variance of the amplitude of the increment of the sample paths. Then we approximate the drift coefficient by combining nonlocal Kramers-Moyal formulas with normalizing flows. Numerical experiments on one-and two-dimensional prototypical examples illustrate the accuracy and effectiveness of our method. This approach will become an effective scientific tool in discovering stochastic governing laws of complex phenomena and understanding dynamical behaviors under non-Gaussian fluctuations.

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Section: Mathematics Subject Classification (2020) Msc 60g51 • Msc 60...mentioning

confidence: 99%

Extracting stochastic dynamical systems with $α$-stable Lévy noise from data

Li,

Lu,

et al. 2021

Preprint

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“…The P(X, t) is probability density function for the solution of Eq. (2.2) with σ = 0 subject to the initial condition X 0 = x 0 , the non-local Fokker-Planck equation for P(X, t) is [34,35]…”

Section: Non-local Fokker-planck Equationmentioning

confidence: 99%

Stochastic Bifurcation in Single-Species Model Induced by α-Stable Levy Noise

Tesfay,

Yuan

et al. 2020

Preprint

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Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic bifurcation techniques are infrequently employed. Here we establish stochastic P-bifurcation behavior of (i) a growth model with state dependent birth rate and constant death rate, and (ii) a logistic growth model with state dependent carrying capacity, both of which are driven by multiplicative symmetric stable Lévy noise. Transcritical bifurcation occurs in the deterministic counterpart of the first model, while saddle-node bifurcation takes place in the logistic growth model. We focus on the impact of the variations of the growth rate, the per capita daily adult mortality rate, the stability index, and the noise intensity on the stationary probability density functions of the associated non-local Fokker-Planck equation. Implications of these bifurcations in population dynamics are discussed. In the first model the bifurcation parameter is the ratio of the population birth rate to the population death rate. In the second model the bifurcation parameter corresponds to the sensitivity of carrying capacity to change in the size of the population near equilibrium. In each case we show that as the value of the bifurcation parameter increases, the shape of the steady-state probability density function changes and that both stochastic models exhibit stochastic Pbifurcation. The unimodal density functions become more peaked around deterministic equilibrium points as the stability index increases. While, an increase in any one of the other parameter has an effect on the stationary probability density function. That means the geometry of the density function changes from unimodal to flat, and its peak appears in the middle of the domain, which means a transition occurs.

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“…In the natural world, there are different types of random noises, such as the well-known white noise, the Lévy jump noise which considers the motivation that the continuity of solutions may be inevitably under severe environmental perturbations, such as earthquakes, floods, volcanic eruptions, SARS, influenza [21][22][23], and a jump process should be introduced to prevent and control diseases, and so on. Mathematically, several authors [24][25][26][27] used the Lévy process to describe the phenomena that cause a big jump to occur occasionally.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

et al. 2021

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For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by ξ which depends on white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that COVID-19 vanishes from the population if $\xi <1$ ξ < 1 ; whereas the epidemic cannot go out of control if $\xi >1$ ξ > 1 . From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.

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Transitions between metastable states in a simplified model for the thermohaline circulation under random fluctuations

Cited by 11 publications

References 22 publications

Extracting stochastic dynamical systems with $α$-stable Lévy noise from data

Extracting stochastic dynamical systems with $α$-stable Lévy noise from data

Stochastic Bifurcation in Single-Species Model Induced by α-Stable Levy Noise

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

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