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 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
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.
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].
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.
