The paper represents very simple procedure of identification, based on step response of the process. Results of identification are extended Strejc＇s models （named ZenanX model, models with n equivalent time constant...The paper represents very simple procedure of identification, based on step response of the process. Results of identification are extended Strejc＇s models （named ZenanX model, models with n equivalent time constants and delay time）. Described mathematically proved equations which show an easy way of filtering and differentiation step response with the help of the data window. It also supports the contention that the point of intersection of tangent to the integrated step response and the X axis represents the sum of time constants and delay time, and showed the method （named ZenoX method） of determining Strej c extended model. For the determination of the impulse response （important for definition of models） are used orthonormal functions （Laguerre）. Simulations are made in the package Matlab. The paper represents results from numerous simulations. The method allows simple and rapid extraction of the Extended Strejc model （ZenanX model）, which is often used to adjust the controllers. Through the simulations of the procedure of removing noise from measured step response is described.展开更多
In this paper, a diffusive hepatitis B virus （HBV） infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intrac...In this paper, a diffusive hepatitis B virus （HBV） infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intracellular delay in the reproduction of infected hepatocytes are taken into account. We define the basic reproduction number R0 that determines the dynamical behavior of the model. The local and global stability of the spatially homogeneous steady states are analyzed by using the linearization technique and the direct Lyapunov method, respectively. It is shown that the susceptible uninfected steady state is globally asymptotically stable whenever R0 ≤i and is unstable whenever R0 〉1. Also, the infected steady state is globally asymptotically stable when R0 〉 1. Finally, numerical simulations are carried out to illustrate the results obtained.展开更多
This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation ph...This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation phenomena： Transcritical bifurcation, singularity induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.展开更多
文摘The paper represents very simple procedure of identification, based on step response of the process. Results of identification are extended Strejc＇s models （named ZenanX model, models with n equivalent time constants and delay time）. Described mathematically proved equations which show an easy way of filtering and differentiation step response with the help of the data window. It also supports the contention that the point of intersection of tangent to the integrated step response and the X axis represents the sum of time constants and delay time, and showed the method （named ZenoX method） of determining Strej c extended model. For the determination of the impulse response （important for definition of models） are used orthonormal functions （Laguerre）. Simulations are made in the package Matlab. The paper represents results from numerous simulations. The method allows simple and rapid extraction of the Extended Strejc model （ZenanX model）, which is often used to adjust the controllers. Through the simulations of the procedure of removing noise from measured step response is described.
文摘In this paper, a diffusive hepatitis B virus （HBV） infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intracellular delay in the reproduction of infected hepatocytes are taken into account. We define the basic reproduction number R0 that determines the dynamical behavior of the model. The local and global stability of the spatially homogeneous steady states are analyzed by using the linearization technique and the direct Lyapunov method, respectively. It is shown that the susceptible uninfected steady state is globally asymptotically stable whenever R0 ≤i and is unstable whenever R0 〉1. Also, the infected steady state is globally asymptotically stable when R0 〉 1. Finally, numerical simulations are carried out to illustrate the results obtained.
基金This work was supported by the National Science Foundation of China under Grant No. 60974004 and Natural Science Foundation of China under Grant No. 60904009.
文摘This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation phenomena： Transcritical bifurcation, singularity induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity induced bifurcation only occurs in singular system and usually links with the expansion of population. When the diffusion is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.
