具有时滞和脉冲输入的一类双资源和两种微生物恒化器模型的分析

考虑一类双资源和两种微生物且具有时滞和脉冲输入的恒化器模型,证明了微生物灭绝周期解的存在性,并得到该周期解全局吸引性的临界条件和系统持久的充分条件,最后利用数值模拟结果说明本文的主要结论.     

Uniform persistence for a discrete predator-prey system with delays

In this paper, we deal with a discrete predator-prey model with monotonic functional responses and give a sufficient condition of uniform persistence for the system.     

Characterization of the photodegradation products of metolachlor: structural elucidation,potential toxicity and persistence

Aqueous solutions of metolachlor and metolachlor‐d₆ were photolyzed with UV‐visible radiations. The structures of 15 by‐products of metolachlor were determined through gas chromatography‐mass spectrometry analyses using electron and chemical ionization combined with multistage mass spectrometry. The photolysis by‐products of metolachlor resulted mainly from dehalogenation and hydroxylation, in some cases accompanied by cyclization. In silico tests for toxicity prediction showed that the toxicity of some photolysis products is expected to be greater than that of metolachlor. Persistence studies showed that the by‐product relative abundances vary in large amounts with the irradiation time. The post‐photolysis evolution of the solution was also studied, in order to determine the persistence of the main by‐products. It allowed to establish that most of the by‐products can be found more than 12 h after the end of the photolysis, which is of a great concern as treated water is generally available for consumption only a few hours after treatment in most of industrial processes. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects

In this paper, we propose a stochastic non-autonomous Lotka–Volterra predator–prey model with impulsive effects and investigate its stochastic dynamics. We first prove that the subsystem of the system has a unique periodic solution which is globally attractive. Furthermore, we obtain the threshold value in the mean which governs the stochastic persistence and the extinction of the prey–predator system. Our results show that the stochastic noises and impulsive perturbations have crucial effects on the persistence and extinction of each species. Finally, we use the different stochastic noises and impulsive effects parameters to provide a series of numerical simulations to illustrate the analytical results.     

Scaling Laws of Bottle‐Brush Polymers in Dilute Solutions

The structural determination and manipulation of bottle‐brush polymers, a class of polymers with serially grafted side‐chains, is challenging due to the interplay of side‐chain and backbone interactions over various length scales. The present work performs a detailed analysis, using molecular dynamics simulation techniques, to unravel these interactions by probing the distinct rod to a flexible real‐chain with self‐avoiding walk (SAW) type crossover in the backbone static structure factor. This analysis elucidates the deviation from flexible chain behavior, while also providing a quantitative measure of persistence length, . Significantly, the results identify a trend in which is consistent with the debated theoretical prediction of , where N_s is the number of monomers in each side‐chain of the bottle‐brush polymer.

     

QUALITATIVE ANALYSIS OF AN SEIS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE

By means of limit theory and Fonda's theorem, an SEIS epidemic model with constant recruitment and the disease-related rate is considered. The incidence term is of the nonlinear form, and the basic reproduction number is found. If the basic reproduction number is less than one, there exists only the disease-free equilibrium, which is globally asymptotically stable, and the disease dies out eventually. If the basic reproduction number is greater than one, besides the unstable disease-free equilibrium, there exists also a unique endemic equilibrium, which is locally asymptotically stable, and the disease is uniformly persistent.     

Un modéle d'lnspections optimales

We consider the following model: we inspect the motion of a Markov process with which an “evolution cost” is associated. We inspect the process at times T ₁…, T _n ,…. If when we inspect, its value is in a given set A, it continues its evolution, otherwise we kill it. At each inspection we associate an "inspection cost" and a "killing cost". The problem consists of finding a sequence of optimal inspections. After the modelization we construct the value function by an iterative procedure as in impulse control theory, by using the theory of analytic functions and theorems of section. Thanks to the criteria of optimality we get a sequence of optimal inspections under very general hypotheses.     

Dynamics in a periodic competitive model with stage structure

In this paper, we consider a time-delayed periodic system which describes the competition among mature populations. By appealing to theories of monotone dynamical systems, periodic semiflows and uniform persistence, we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion.     

SEIRS型传染病模型的全局稳定性

In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.     

Uniform persistence of asymptotically periodic multispecies competition predator–prey systems with Holling III type functional response

In this paper, we studied the persistence of the asymptotically periodic multispecies competition predator–prey system with Holling III type functional response. Further, by use of the Standard Comparison Theorem, we improved the results of paper [C. Chen, F. Chen, Conditions for global attractivity of multispecies ecological competition-predator system with Holling III type functional response, Journal of Biomathematics 19(2) (2004) 136–140].