In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start wi...In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.展开更多
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix i...This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.展开更多
So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It...So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.展开更多
文摘In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.
基金This work was supported by the National Natural Science Foundation of China(No.60474013)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050424002)the Doctoral Foundation of Shandong Province (No. 2004BS01010)
文摘This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
基金Supported by the National Natural Science Foundation of China(Grant No.60574042)
文摘So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.
