The application of a standard Galerkin finite element method for convection-diffusion problems leads to oscillations in the discrete solution, therefore stabilization seems to be necessary. We discuss several recent s...The application of a standard Galerkin finite element method for convection-diffusion problems leads to oscillations in the discrete solution, therefore stabilization seems to be necessary. We discuss several recent stabilization methods, especially its combination with a Galerkin method on layer-adapted meshes. Supercloseness results obtained allow an improvement of the discrete solution using recovery techniques.展开更多
A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission ra...A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that media coverage exhibits its effect only when the number of the infected exceeds a certain critical level. Further, it is assumed that the impact of media coverage on the contact transmission is described by an exponential decreasing factor. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity and media coverage impact is sufficiently small, a unique endemic equilibrium exists, which is globally asymptotically stable.展开更多
In this paper, a HTLV-I infection model with two delays is considered. It is found that the dynamics of this model are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection a...In this paper, a HTLV-I infection model with two delays is considered. It is found that the dynamics of this model are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0 〈 1, the infection-free equilibrium P0 is globally asymptotically stable. If R1 〈 1 〈 R0, the asymptomatic-carrier equilibrium P1 is globally asymptotically stable. If R1 〉 1, there exists a unique HAM/TSP equilibrium P2. The stability of P2 is changed when the second delay T2 varies, that is there exist stability switches for P2.展开更多
In this paper, the sharp threshold properties of a （2n ＋ 1）-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected tar- get cells, n classes of infected cells a...In this paper, the sharp threshold properties of a （2n ＋ 1）-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected tar- get cells, n classes of infected cells and nonlinear incidence rate h（x,v）. Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model.展开更多
In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple ...In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural net- works, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.展开更多
文摘The application of a standard Galerkin finite element method for convection-diffusion problems leads to oscillations in the discrete solution, therefore stabilization seems to be necessary. We discuss several recent stabilization methods, especially its combination with a Galerkin method on layer-adapted meshes. Supercloseness results obtained allow an improvement of the discrete solution using recovery techniques.
文摘A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that media coverage exhibits its effect only when the number of the infected exceeds a certain critical level. Further, it is assumed that the impact of media coverage on the contact transmission is described by an exponential decreasing factor. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity and media coverage impact is sufficiently small, a unique endemic equilibrium exists, which is globally asymptotically stable.
基金Acknowledgments The authors would like to thank the reviewers＇ constructive suggestions which have improved the presentation of the paper. This research is supported by National Natural Science Foundation of China （No. 11371111）, the Research Fund for the Doctoral Program of Higher Education of China （No. 20122302110044） and Shandong Provincial Natural Science Foundation, China （No. ZR2013AQ023）.
文摘In this paper, a HTLV-I infection model with two delays is considered. It is found that the dynamics of this model are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0 〈 1, the infection-free equilibrium P0 is globally asymptotically stable. If R1 〈 1 〈 R0, the asymptomatic-carrier equilibrium P1 is globally asymptotically stable. If R1 〉 1, there exists a unique HAM/TSP equilibrium P2. The stability of P2 is changed when the second delay T2 varies, that is there exist stability switches for P2.
基金The authors would like to thank the anonymous referees and the editor for very helpful suggestions and comments which led to improvements of our orig- inal paper. J. Wang was supported by National Natural Science Foundation of China （Nos. 11401182 and 11471089）, Natural Science Foundation of Heilongjiang Province （No. A201415）, Science and Technology Innovation Team in Higher Edu- cation Institutions of Heilongjiang Province （No. 2014TD005）, Project funded by China Postdoctoral Science Foundation （No. 2014M552295） and Project funded by Chongqing Postdoctoral Foundation （No. Xm2014024）. X. Wang is supported by the National Natural Science Foundation of China （No. 11301453）, Postdoctoral Science Foundation of China （No. 2014M562366）, Postdoctoral Science Foundation of Shaanxi Province （No. 2014010）, the Universities Young Teachers Program of Henan Province （No. 2014GGJS-093）.
文摘In this paper, the sharp threshold properties of a （2n ＋ 1）-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected tar- get cells, n classes of infected cells and nonlinear incidence rate h（x,v）. Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model.
文摘In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural net- works, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.
