Modeling and Dynamic Analysis in a Hybrid Stochastic Bioeconomic System with Double Time Delays and Lévy Jumps by Chao Liu, Longfei Yu, Luping Wang

“…By constructing appropriate Lyapunov functions, asymptotic dynamic behavior of the proposed hybrid stochastic system with double time delays and Lévy jumps is discussed. …”
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The Threshold of a Stochastic SIRS Model with Vertical Transmission and Saturated Incidence by Chunjuan Zhu, Guangzhao Zeng, Yufeng Sun

“…If the noise is small, it is shown that the threshold of the stochastic system determines the extinction and persistence of the epidemic. …”
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Stochastic and deterministic models for agricultural production networks by P. Bai, H.T. Banks, S. Dediu, A.Y. Govan, M. Last, A.L. Lloyd, H.K. Nguyen, M.S. Olufsen, G. Rempala, B.D. Slenning

“…A stochastic modeland its approximate deterministic model for averages over samplepaths of the stochastic system are developed. Simulations,sensitivity and generalized sensitivity analyses are given.Finally, it is shown how diseases may be introduced into thenetwork and corresponding simulations are discussed.…”
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Dynamic Analysis of Stochastic Lotka–Volterra Predator-Prey Model with Discrete Delays and Feedback Control by Jinlei Liu, Wencai Zhao

“…Further, we investigate the asymptotic property of stochastic system at the positive equilibrium point of the corresponding deterministic model and establish sufficient conditions for the persistence and extinction of the model. …”
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Asymptotic Behavior of a Stochastic Delayed Model for Chronic Hepatitis B Infection by Bo Wu, Jianwen Jia

“…Secondly, the sufficient conditions are derived that the solution of the stochastic system fluctuates around the disease-free equilibrium E0 and the endemic equilibrium E∗. …”
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Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate by Chaoqun Xu, Sanling Yuan, Tonghua Zhang

“…Furthermore, the sufficient conditions for persistence in the mean of the stochastic system and washout of the microorganism are obtained. …”
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Stabilization for the Stochastic Heat Equation with Boundary Control by Baolin Ma, Yiyue Sun, Guojie Zheng

“…By the backstepping technique, a boundary feedback control is designed to stabilize the unstable stochastic system, including the 2nd-moment and almost-sure exponential stabilization. …”
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Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control by Fathalla A. Rihan, Chinnathambi Rajivganthi, Palanisamy Muthukumar

“…We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. …”
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Multiple-Model Adaptive Estimation with A New Weighting Algorithm by Weicun Zhang, Sufang Wang, Yuzhen Zhang

“…The state estimation of a complex dynamic stochastic system is described by a discrete-time state-space model with large parameter (including the covariance matrices of system noises and measurement noises) uncertainties. …”
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Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory by Ruofeng Rao, Shouming Zhong

“…The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. …”
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Spin Polarization Oscillations and Coherence Time in the Random Interaction Approach by P. Pereyra

“…We apply the Extended Gaussian Orthogonal Ensemble approach to model the stochastic system-environment interaction and calculate the survival and spin polarization to first and second order of the interaction picture. …”
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Development of Driver-Behavior Model Based onWOA-RBM Deep Learning Network by Junhui Liu, Yajuan Jia, Yaya Wang

“…Human drivers’ behavior, which is very difficult to model, is a very complicated stochastic system. To characterize a high-accuracy driver behavior model under different roadway geometries, the paper proposes a new algorithm of driver behavior model based on the whale optimization algorithm-restricted Boltzmann machine (WOA-RBM) method. …”
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Vibration Analysis of a Piecewise-Smooth System with Negative Stiffness under Delayed Feedback Control by Dongmei Huang, Wei Li, Guidong Yang, Meijuan He, Hong Dang

“…The amplitude-frequency response and steady-state moments together with the corresponding stability conditions of the controlled stochastic system are derived, in which the degradation case is also under consideration. …”
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Bounding the Inefficiency of the Multiclass, Multicriteria C-Logit Stochastic User Equilibrium in a Transportation Network by Lekai Yuan, Xi Zhang, Chaofeng Shi

“…., to compare multiclass CL-SUE with multiclass system optimum, or to compare multiclass CL-SUE with multiclass C-Logit stochastic system optimum (CL-SSO), under the time-based criterion and the monetary-based criterion, respectively. …”
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On the mathematical modelling of tumor-induced angiogenesis by Luis L. Bonilla, Vincenzo Capasso, Mariano Alvaro, Manuel Carretero, Filippo Terragni

“…On the other hand we have shown that ensemble averages over many realizations of the stochastic system may better correspond to a deterministic reaction-diffusion system.…”
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Dynamical Behavior of the SEIS Infectious Disease Model with White Noise Disturbance by Yuheng Song, Qixing Han

“…In addition, we show that the stochastic system exists a unique positive global solution. …”
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A retrial queueing system with processor sharing and impatient customers by V. I. Klimenok

“…The problem of constructing and investigating a mathematical model of a stochastic system with processor sharing, repeated calls, and customer impatience is considered. …”
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