Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process

Ayoubi, Tawfiqullah; Bao, Haibo

doi:10.1016/j.amc.2020.125465

Cited by 12 publications

(5 citation statements)

References 28 publications

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“…Sadece eklemli robotlarda değil aynı zamanda doğrusal olmayan bir sistem olan insansız hava aracı gibi sistemlerde irtifa kontrolü DDPG yardımı ile gerçekleştirilmiştir [9]. Ornstein-Uhlenbeck süreci (OUS), matematikten [10] enerjiye [11] kadar birçok alanda sıklıkla kullanılan skolastik türev işlemidir. Yapılan bir çalışmada, OUS kullanılarak rüzgâr gücünün tahmini çalışılmıştır [11].…”

Section: Ddpg Algoritmasında Bulunan Ornstein-uhlenbeckunclassified

DDPG Algoritmasında Bulunan Ornstein–Uhlenbeck Gürültüsünün Standart Sapmasının Araştırılması

Bingöl

2021

Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım Ve Teknoloji

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Reinforcement learning is a learning method that many creatures often unwittingly use to gain abilities such as eating and walking. Inspired by this learning method, machine learning researchers have reduced this learning method to subheadings as value learning and policy learning. In this study, the noise standard deviation of the deep deterministic policy gradient (DDPG) method, which is one of the policy learning algorithms, was examined to solve inverse kinematics of a 2 degrees-of-freedom planar robot. For this examination, 8 different functions were determined depending on the maximum value of the output of the action artificial neural network. Created artificial neural networks were trained by using these functions in 1000 iterations with 200 steps in each iteration. After the training, the statistical difference between the groups was examined and it was found that there was no statistical difference between the three best groups. For this reason, the best three groups were retrained 2500 iterations and 200 steps and tested for 100 different test scenarios after the training. After testing, the inverse kinematic equation of the 2 degrees-of-freedom planar robot with minimal errors was obtained with the help of artificial neural networks. In the light of the results, the importance of the choice of the standard deviation of noise and the correct range of selection was presented for researchers who will work in this field.

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Section: Ddpg Algoritmasında Bulunan Ornstein-uhlenbeckunclassified

DDPG Algoritmasında Bulunan Ornstein–Uhlenbeck Gürültüsünün Standart Sapmasının Araştırılması

Bingöl

2021

Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım Ve Teknoloji

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“…Indeed, since the continuous spectrum of environmental noise, many parameters involved in infectious disease systems, such as transmission rates, mortality rates and so on, should fluctuate randomly around their mean [9][10][11][12][13][14][15]. Zhang et al [8] pointed out there are two methods to perturb parameters in the literature, one is linear Gaussian white noise [14,15] and the other is the meanreverting Ornstein-Uhlenbeck process.…”

Section: Introductionmentioning

confidence: 99%

“…In [13], Zhou et al obtained thresholds of extinction and persistence for a stochastic SIR epidemic model with mean-reverting Ornstein-Uhlenbeck process, and proved the existence of a unique density function. Inspired by the method of [9][10][11][12][13], in this work, we formulate an SIHR epidemic model with general population-size dependent contact rate and mean-reverting Ornstein-Uhlenbeck process.…”

Section: Introductionmentioning

confidence: 99%

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A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis

Mu,

Jiang

2024

Nonlinear Dyn

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The purpose of this work is to investigate a novel stochastic SIHR epidemic model, which includes a general incidence rate and mean-reversion Ornstein-Uhlenbeck process. Firstly, the existence of global positivity of the solution is testified by Lyapunov function. Secondly, this disease will be eradicated if R s 0 < 1. Otherwise, if R * 0 > 1, then the system has a stationary distribution, which means that the pandemic will persist. In addition, an explicit expression of the probability density function for a linear system near quasi-endemic equilibrium is obtained under certain conditions.Finally, a series of numerical simulations are carried out to validate the theoretical conclusions.

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“…This causes a unreasonable result that the variance σ 2 T → +∞ as T → 0, meaning that the modified parameter β(t) will drastically change in a short period which conflicts with continuous environment. To deal with this shortcoming, various stochastic models adapt the assumption that the modified parameter satisfies the mean-reversing process [24,25,26,27] instead of the linear functions of white noise. Inspired by these brilliant ideas, in this paper, we suppose that the transmission rate β is the log-normal Ornstein-Uhlenbeck process, that is to say…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and numerical simulation of a stochastic influenza transmission model with human mobility and Ornstein-Uhlenbeck process

Zhang,

Su,

Jiang

2023

Preprint

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With the inevitable environmental perturbations and complex population movements, the analysis of troublesome influenza is harder to proceed. Studies about the epidemic mathematical models can not only forecast the development trend of influenza, but also have a beneficial influence on the protection of health and the economy. Motivated by this, a stochastic influenza model incorporating human mobility and the Ornstein-Uhlenbeck process is established in this paper. Based on the existence of the unique global positive solution, we obtain sufficient conditions for influenza extinction and persistence, which are related to the basic reproduction number in the corresponding deterministic model. Notably, the analytical expression of the probability density function of stationary distribution near the quasi-endemic equilibrium is obtained by solving the challenging Fokker–Planck equation. Finally, numerical simulations are performed to support the theoretical conclusions, and the effect of main parameters and environmental perturbations on influenza transmission are also investigated.

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Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process

Cited by 12 publications

References 28 publications

DDPG Algoritmasında Bulunan Ornstein–Uhlenbeck Gürültüsünün Standart Sapmasının Araştırılması

DDPG Algoritmasında Bulunan Ornstein–Uhlenbeck Gürültüsünün Standart Sapmasının Araştırılması

A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein–Uhlenbeck process: dynamics analysis

Dynamical analysis and numerical simulation of a stochastic influenza transmission model with human mobility and Ornstein-Uhlenbeck process

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