In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species ca...In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved that the system is uniformly persistent under any dispersion rate effect. Furthermore~ some sufficient conditions are established for the existence of a unique almost periodic solution of the system. The example shows that the criteria in the paper are new, general and easily verifiable.展开更多
In this paper, we construct a composite Milstein method for nonlinear stochastic differential delay equations. Then we analyze the mean square stability for this method and obtain the step size condition under which t...In this paper, we construct a composite Milstein method for nonlinear stochastic differential delay equations. Then we analyze the mean square stability for this method and obtain the step size condition under which the composite Milstein method is mean square stable. Moreover, we get the step size condition under which the composite Milstein method is global mean square stable. A nonlinear test stochastic differential delay equation is given for numerical tests. The results of numerical tests verify the theoretical results proposed.展开更多
In this paper,a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19.The basic reproduction number is calculated using the next gener...In this paper,a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19.The basic reproduction number is calculated using the next generation matrix method.First,the existence of equilibrium points is investigated,and different kinds of equilibrium points indicate that the disease may disappear,or exist that result in different quantity of susceptible individuals,pre-symptomatic infected individuals and symptomatic infected individuals.The stability of the equilibria is discussed by a geometric approach,and it is found that controlling reproduction number to be lower than 1 is not suficient for eradication of COVID-19.Second,transcritical bifurcation is explored,and it is found that improving the ratio of exogenous reinfection may lead to backward bifurcation under poor medical conditions,which indicates that two endemic equilibrium points appear.Third,to investigate the infuence of parameters on the basic reproduction,sensitivity analysis is done to choose relatively sensitive parameters,and the parameters for treatment and media coverage are selected.An optimal control model is established to balance the treatment and media awareness.By exploring the existence and the uniqueness of the optimal control solution,the optimal control strategies are given.Finally,we run numerical simulations to verify the theoretical analysis on actual data of China,and the data from the four different states of India is used for forecasting the situation of infected individuals in a short period.It is found by the simulation that the co-function of treatment and media coverage results in the reduced number of infectious individuals.展开更多
The least-squares (LS) algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the we...The least-squares (LS) algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares (WLS) algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for adaptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller, this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense.展开更多
In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot d...In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot diffuse. We prove that the systems can have aunique positive almost periodic solution, which is globally uniformly asymptotically stableunder some appropriate conditions. In particular, if the system is a periodic system of period ω, it can have a positive globally uniformly asymptotically stable periodic solution ofperiod ω, which is a generalization of Theorem 4 in paper [6].展开更多
We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment.The treatment rate has at most a finite number of jump discontinuities in every compact interv...We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment.The treatment rate has at most a finite number of jump discontinuities in every compact interval.By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis,the basic reproductive number Ro is proved to be a sharp threshold value which completely determines the dynamics of the model.If Ro<1,then there exists a disease-free equilibrium which is globally stable.If Ro>1,the disease-free equilibrium becomes unstable and there exists an endemic equilibrium which is globally stable.We discuss that the disease will die out in a finite time which is impossible for the corresponding SEIR model with continuous treatment.Furthermore,the numerical simulations indicate that strengthening treatment measure after infective individuals reach some level is beneficial to disease control.展开更多
In this paper, we study the BAM neural networks with variable coefficients and delays. By using the Banach fixed point theorem and constructing suitable Lyapunov function, we obtain some sufficient conditions ensuring...In this paper, we study the BAM neural networks with variable coefficients and delays. By using the Banach fixed point theorem and constructing suitable Lyapunov function, we obtain some sufficient conditions ensuring the existence, uniqueness and global stability of periodic solution. These results are helpful to design global exponential stable BAM networks and periodic oscillatory BAM networks.展开更多
This paper proves that difference equation(1.1)is permanent and every solution of equationoscillates about the eauilibrium JSufficient conditions of which the equilibrium x is blobally asymptotically stable are alsoob...This paper proves that difference equation(1.1)is permanent and every solution of equationoscillates about the eauilibrium JSufficient conditions of which the equilibrium x is blobally asymptotically stable are alsoobtained.展开更多
This paper investigates the globally asymptotically stable and L_(2)-gain of robust H_(∞)control for switched nonlinear systems under sampled data.By considering the relationship between the sampling period and the d...This paper investigates the globally asymptotically stable and L_(2)-gain of robust H_(∞)control for switched nonlinear systems under sampled data.By considering the relationship between the sampling period and the dwell time,the non-switching and one switching are discussed in the sampling interval,respectively.Firstly,a state feedback sampled-data controller is constructed by the back-stepping method,and the switching converts to asynchronous switching if it happens within the sampling interval.Then,under the limiting conditions of the sampling period,which are obtained by the average dwell time method,the closed-loop system is globally asymptotically stable and has L_(2)-gain.Finally,two numerical examples are provided to demonstrate the effectiveness of the proposed method.展开更多
In this paper,certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated.For the viral model with a single strain,we have proved the well-posedness and studied ...In this paper,certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated.For the viral model with a single strain,we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number R_(0) and structuring proper Lyapunov functional.Moreover,we found that the infection-free equilibrium is globally asymptotically stable if R_(0)<1,and the infection equilibrium is globally asymptotically stable if R_(0)>1.For the multi-strain model,we found that all viral strains coexist if the corresponding basic reproductive number R^(e)_(j)>1,while virus will extinct if R^(e)_(j)<1.As a result,we found that delay and the density-dependent diffusion does not influence the global stability of the model with cell-to-cell infection and homogeneous Neumann boundary conditions.展开更多
A dynamical system for computing the elliptic boundary problem is presented.It is shown that the proposed system is globally asymptotically stable.The system can be simulated by a neural network.Simulation results are...A dynamical system for computing the elliptic boundary problem is presented.It is shown that the proposed system is globally asymptotically stable.The system can be simulated by a neural network.Simulation results are valid and satisfactory.展开更多
A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated ...A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results arc stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.展开更多
We consider the three species predator-prey model with the same intrinsic growth rates, where species 3 feeds on species 2, species 2 feeds on species 1, species 1 feeds on species 3. An open question raised by Nishan...We consider the three species predator-prey model with the same intrinsic growth rates, where species 3 feeds on species 2, species 2 feeds on species 1, species 1 feeds on species 3. An open question raised by Nishan Krikorian is answered: We obtain the necessary and sufficient conditions for all the orbits to be unbounded. We also obtain the necessary and sufficient conditions for the positive equilibrium to be globally stable. It is shown that there exists a family of neutrally stable periodic orbits, in which we extend Darboux method to three-species models for the first time.展开更多
基金Supported-by the Start-up Fund of Jimei University(ZB2004009)
文摘In this paper, a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied, where all parameters are time-dependent. In this system consisting of n-patches the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved that the system is uniformly persistent under any dispersion rate effect. Furthermore~ some sufficient conditions are established for the existence of a unique almost periodic solution of the system. The example shows that the criteria in the paper are new, general and easily verifiable.
基金Supported by National Natural Science Foundation of China(No.61272024)Anhui Provincial Natural Science Foundation(No.11040606M06)
文摘In this paper, we construct a composite Milstein method for nonlinear stochastic differential delay equations. Then we analyze the mean square stability for this method and obtain the step size condition under which the composite Milstein method is mean square stable. Moreover, we get the step size condition under which the composite Milstein method is global mean square stable. A nonlinear test stochastic differential delay equation is given for numerical tests. The results of numerical tests verify the theoretical results proposed.
基金This research is supported by the Natural Science Foundation of Beijing Municipality(No.4202025).
文摘In this paper,a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19.The basic reproduction number is calculated using the next generation matrix method.First,the existence of equilibrium points is investigated,and different kinds of equilibrium points indicate that the disease may disappear,or exist that result in different quantity of susceptible individuals,pre-symptomatic infected individuals and symptomatic infected individuals.The stability of the equilibria is discussed by a geometric approach,and it is found that controlling reproduction number to be lower than 1 is not suficient for eradication of COVID-19.Second,transcritical bifurcation is explored,and it is found that improving the ratio of exogenous reinfection may lead to backward bifurcation under poor medical conditions,which indicates that two endemic equilibrium points appear.Third,to investigate the infuence of parameters on the basic reproduction,sensitivity analysis is done to choose relatively sensitive parameters,and the parameters for treatment and media coverage are selected.An optimal control model is established to balance the treatment and media awareness.By exploring the existence and the uniqueness of the optimal control solution,the optimal control strategies are given.Finally,we run numerical simulations to verify the theoretical analysis on actual data of China,and the data from the four different states of India is used for forecasting the situation of infected individuals in a short period.It is found by the simulation that the co-function of treatment and media coverage results in the reduced number of infectious individuals.
基金the National Natural Science Foundation of China(No.60474026)the Asia Research Center at Tsinghua University
文摘The least-squares (LS) algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares (WLS) algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for adaptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller, this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense.
文摘In this paper, we consider two-species n-patch almost periodic competitive systemswith diffusion, where one species can diffuse between any two of n patches, but the otheris confined to one of the patches and cannot diffuse. We prove that the systems can have aunique positive almost periodic solution, which is globally uniformly asymptotically stableunder some appropriate conditions. In particular, if the system is a periodic system of period ω, it can have a positive globally uniformly asymptotically stable periodic solution ofperiod ω, which is a generalization of Theorem 4 in paper [6].
基金supported by the National Nature Science Foundation of China(11271154).
文摘We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment.The treatment rate has at most a finite number of jump discontinuities in every compact interval.By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis,the basic reproductive number Ro is proved to be a sharp threshold value which completely determines the dynamics of the model.If Ro<1,then there exists a disease-free equilibrium which is globally stable.If Ro>1,the disease-free equilibrium becomes unstable and there exists an endemic equilibrium which is globally stable.We discuss that the disease will die out in a finite time which is impossible for the corresponding SEIR model with continuous treatment.Furthermore,the numerical simulations indicate that strengthening treatment measure after infective individuals reach some level is beneficial to disease control.
基金Supported by the NNSF of China (10371034)Foundation for University Key Teacher by the Ministry of Education of China and also by the Foundation of professor project of Chenzhou Teachers College.
文摘In this paper, we study the BAM neural networks with variable coefficients and delays. By using the Banach fixed point theorem and constructing suitable Lyapunov function, we obtain some sufficient conditions ensuring the existence, uniqueness and global stability of periodic solution. These results are helpful to design global exponential stable BAM networks and periodic oscillatory BAM networks.
文摘This paper proves that difference equation(1.1)is permanent and every solution of equationoscillates about the eauilibrium JSufficient conditions of which the equilibrium x is blobally asymptotically stable are alsoobtained.
文摘This paper investigates the globally asymptotically stable and L_(2)-gain of robust H_(∞)control for switched nonlinear systems under sampled data.By considering the relationship between the sampling period and the dwell time,the non-switching and one switching are discussed in the sampling interval,respectively.Firstly,a state feedback sampled-data controller is constructed by the back-stepping method,and the switching converts to asynchronous switching if it happens within the sampling interval.Then,under the limiting conditions of the sampling period,which are obtained by the average dwell time method,the closed-loop system is globally asymptotically stable and has L_(2)-gain.Finally,two numerical examples are provided to demonstrate the effectiveness of the proposed method.
基金supported by NSFC(Nos.11671346 and U1604180)Key Scien-tific and Technological Research Projects in Henan Province(Nos.192102310089,18B110003)+1 种基金Foundation of Henan Educational Committee(No.19A110009)Grant of Bioinformatics Center of Henan University(No.2019YLXKJC02).
文摘In this paper,certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated.For the viral model with a single strain,we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number R_(0) and structuring proper Lyapunov functional.Moreover,we found that the infection-free equilibrium is globally asymptotically stable if R_(0)<1,and the infection equilibrium is globally asymptotically stable if R_(0)>1.For the multi-strain model,we found that all viral strains coexist if the corresponding basic reproductive number R^(e)_(j)>1,while virus will extinct if R^(e)_(j)<1.As a result,we found that delay and the density-dependent diffusion does not influence the global stability of the model with cell-to-cell infection and homogeneous Neumann boundary conditions.
文摘A dynamical system for computing the elliptic boundary problem is presented.It is shown that the proposed system is globally asymptotically stable.The system can be simulated by a neural network.Simulation results are valid and satisfactory.
基金the K.C. Wong Education Foundation, Hong Kong and Partly by the China Postdoctoral Science Foundation.
文摘A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results arc stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.
文摘We consider the three species predator-prey model with the same intrinsic growth rates, where species 3 feeds on species 2, species 2 feeds on species 1, species 1 feeds on species 3. An open question raised by Nishan Krikorian is answered: We obtain the necessary and sufficient conditions for all the orbits to be unbounded. We also obtain the necessary and sufficient conditions for the positive equilibrium to be globally stable. It is shown that there exists a family of neutrally stable periodic orbits, in which we extend Darboux method to three-species models for the first time.