A note on “Existence and uniqueness of coexistence states for an elliptic system coupled in the linear part”, by Hei Li-jun,Nonlinear Anal. Real World Appl. 5, 2004

In this short paper I report on a paper published in Nonlinear Analysis: Real World Applications in 2004. There is a major mistake early in that paper which makes most of its claims false. The class of reaction–diffusion systems considered in the paper has been the object of a renewed investigation in the past few years, by myself and others, and recent discoveries provide explicit counter-examples.     

The classification for dynamics of an STD model

In this paper, a 3(n+1) dimensional sexually transmitted disease model is studied. The model involves two competing strains 1 and 2, where females are divided into n different groups based on their susceptibility to two distinct pathogenic strains. The first and second reproduction numbers , which have their biological meaning, are defined for strain , respectively. With the non-degeneracy assumption (H), a complete classification for dynamics of this model in terms of is presented, which is based on the theory of type-K monotone dynamical systems.     

Excess molar heat capacity of isobutyric acid–water binary liquid mixtures near and far away from the critical temperature

The heat capacity of the liquid–liquid mixture isobutyric acid–water has been measured for the first time near and far away from its critical point using an adiabatic calorimeter. The measurements were performed at atmospheric pressure, in the one phase region as a function of three temperatures: (1) T − T_C = 0.055 °C, (2) T − T_C = 3.055 °C, (3) T − T_C = 8.055 °C and of the composition X in acid (IA). The heat capacity C_p decreases rapidly when X increases at the used temperatures. Near the critical composition, C_p is not affected by the correlation of the concentration fluctuations.

The molar excess heat capacity of the system under investigation was analysed along the phase diagram and considered as a structural transformation effect.     

Stable coexistence mediated by specialist harvesting in a two zooplankton–phytoplankton system

This paper deals with a predator–prey model with specialist harvesting, representing a two predators (Zooplankton) and one resource (Phytoplankton) system. First, the existence and stability of equilibria is analyzed both from local and global point of view. Our results indicate that a specialist harvesting which is discriminate may mediate the coexistence of the two zooplankton species which competitively exclude each other in absence harvesting. Although in most cases increasing harvesting reduces the two zooplankton species numbers, when harvesting leads to coexistence, it may also lead to increase the two zooplankton species numbers. Furthermore, to protect fish population from over exploitation a control instrument tax is imposed. The problem of optimal taxation policy is then solved by using Pontryagin’s maximal principle. It is established that the zero discounting leads to the maximization of the net economic revenue to the society and an infinite discount rate leads to complete dissipation of the net economic revenue to the society. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings.     

Existence of the solutions of a reaction cross-diffusion model for two species

In this paper, we investigate a two-cooperative species model with reaction cross-diffusion under the Dirichlet boundary value condition. By applying Lyapunov–Schmidt reduction method and some important formulas, we obtain the existence of coexistence solutions under some given conditions.     

Global directed dynamics of a Lotka–Volterra competition-diffusion system

In this study, we consider a directed–diffusion system describing the interactions between two organisms in heterogeneous environment. We first establish a linearly stability of the co-existence (positive) steady state. Then we further present a classification on all possible long-time dynamical behaviors by appealing to the theory of monotone dynamical systems.     

Coexistence in a two species chemostat model with Markov switchings

This paper formulates a new switched two species chemostat model and discusses the coexistence behavior in the chemostat. A complete classification on the single-species chemostat is carried out firstly, where the stationary distribution with ergodicity is derived to exist and be unique. Then, based on the obtained stationary distribution and the comparison theorem, we put forward some sufficient conditions for the coexistence of microorganisms in the two species chemostat with Markov switchings. Moreover, when the species coexist in the deterministic chemostat for each state and have the same break-even concentrations for all states, they are proved to coexist still in the switched chemostat, which randomized the results of the classical deterministic chemostat. Results in this paper show that Markov switchings can contribute to coexistence of the two species.     

基于少模光纤单模工作的量子-经典信号同传

考虑到少模光纤单模工作时具有低非线性以及损耗、色散保持特性,提出基于少模光纤单模工作的量子-经典信号同传方案.使用Optisystem构建了基于少模光纤单模工作的量子-经典信号同传模型,分析了其传输性能,并与现有的基于单模光纤的量子-经典信号同传模型进行了对比.结果表明所提模型可以有效降低现有模型中的非线性效应和信号串扰,将误比特率降低了两个数量级,显著提高了信号的传输质量,可用于量子保密通信大规模网络化.     

Global dynamics of a predator-prey model

This paper deals with the dynamics of a predator-prey model with Hassell-Varley-Holling functional response. First, we show that the predator coexists with prey if and only if predator's growth ability is greater than its death rate. Second, using a blow-up technique, we prove that the origin equilibrium point is repelling and extinction of both predator and prey populations is impossible. Third, the local and global stability of the positive steady state coincide when the predator interference is large. Finally, for a typical biological case, we show instability of the positive equilibrium implies global stability of the limit cycle. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.