The Lotka-Volterra Competition System with Discrete and Distributed Time Delays

In this paper, the Lotka-Volterra competition system with discrete and distributed time delays is considered. By analyzing the characteristic equation of the linearized system, the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don＇t effect the stability of the equilibrium in the delay system. Finally, we can conclude that the positive equilibrium is global asymptotically stable in the delay system.

Stability of stochastic switched epidemic systems with discrete or distributed time delay

Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.

Global dynamics for a live-virus-blood model with distributed time delay

In this paper, the global properties of a mathematical modeling of hepatitis C virus （HCV） with distributed time delays is studied. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states. It is shown that if the basic reproduction number R0 is less than unity, then the uninfected steady state is globally asymptotically stable. If the basic reproduction number R0 is larger than unity, then the infected steady state is globally asymptotically stable.

VIRAL DYNAMICS IN A DISTRIBUTED TIME DELAYED HCV PATHOGENESIS MODEL

In this paper, we investigate global dynamics for a distributed time delayed HCV infec tion model. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. By employing the method of Lyapunov functional, we prove that the uninfected equilibrium is global asymptotically stable if the basic reproduction number is less than one, it is unsta ble and the infected equilibrium is global asymptotically stable if the basic reproduction number is larger than one. The simulations results are in good accordance with our analytic results.

Applying the Different Statistical Tests in Analysis of Electrical Breakdown Mechanisms in Nitrogen Filled Gas Diode

This paper presents the results of our investigations of breakdown mechanisms, as well as a description of their influence on the distributions of time delay distributions, for a gas tube filled with nitrogen at 4 mbar. The values of the time delay are measured for different voitages, and the values of the relaxation times and their distributions and probability plots are analyzed. The obtained density distributions have Gaussian distributions and exponential distributions for different values of relaxation times （Gaussian for small values and exponential for large values of relaxation time）. It is shown that for middle values of relaxation time the delay distributions have a shape between Caussian and exponential distributions, which is a result of the different influences of electrical breakdown.

A class of anomalous diffusion epidemic models based on CTRW and distributed delay

In recent years,the epidemic model with anomalous diffusion has gained popularity in the literature.However,when introducing anomalous diffusion into epidemic models,they frequently lack physical explanation,in contrast to the traditional reaction-diffusion epidemic models.The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable.Specifically,based on the continuous-time random walk(CTRW),starting from two stochastic processes of the waiting time and the step length,time-fractional space-fractional diffusion,timefractional reaction-diffusion and fractional-order diffusion can all be naturally introduced into the SIR(S:susceptible,I:infectious and R:recovered)epidemic models,respectively.The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays.Distributed time delay systems can also be reduced to existing models,such as the standard SIR model,the fractional infectivity model and others,within the proper bounds.Meanwhile,as an application of the above stochastic modeling method,the physical meaning of anomalous diffusion is also considered by taking the SEIR(E:exposed)epidemic model as an example.Similar methods can be used to build other types of epidemic models,including SIVRS(V:vaccine),SIQRS(Q:quarantined)and others.Finally,this paper describes the transmission of infectious disease in space using the real data of COVID-19.

Performance Comparison of Artificial Neural Network Models for Daily Rainfall Prediction

With an aim to predict rainfall one-day in advance, this paper adopted different neural network models such as feed forward back propagation neural network （BPN）, cascade-forward back propagation neural network （CBPN）, distributed time delay neural network （DTDNN） and nonlinear autoregressive exogenous network （NARX）, and compared their forecasting capabilities. The study deals with two data sets, one containing daily rainfall, temperature and humidity data of Nilgiris and the other containing only daily rainfall data from 14 rain gauge stations located in and around Coonoor （a taluk of Nilgiris）. Based on the performance analysis, NARX network outperformed all the other networks. Though there is no major difference in the performances of BPN, CBPN and DTDNN, yet BPN performed considerably well confirming its prediction capabilities. Levenberg Marquardt proved to be the most effective weight updating technique when compared to different gradient descent approaches. Sensitivity analysis was instrumental in identifying the key predictors.

THE GLOBAL STABILITY OF A COMPETING CHEMOSTAT MODEL WITH DELAYED NUTRIENT RECYCLING

In this paper, by applying the method of Liapunov functionals we study the global stability of the positive equilibrium of a competing chemostat model with delayed nutrient recycling. The sufficient conditions of the global stability (involved in average time delay or not) are obtained.