Note on the Stability Property of a Cooperative System Incorporating Harvesting

The stability of a kind of cooperative model incorporating harvesting is revisited in this paper. By using an iterative method, the global attractivity of the interior equilibrium point of the system is investigated. We show that the condition which ensures the existence of a unique positive equilibrium is enough to ensure the global attractivity of the positive equilibrium. Our results significantly improve the corresponding results o

Almost periodic solution of a discrete competitive system with delays and feedback controls

A discrete nonlinear almost periodic multispecies competitive system with delays and feedback controls is proposed and investigated. We obtain sufficient conditions to ensure the permanence of the system. Also, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. In additional, an example together with its numerical simulation are presented to illustrate the feasibility of the main result

Global Attractivity in a Discrete Mutualism Model with Infinite Deviating Arguments

A set of sufficient conditions is obtained for the global attractivity of the following two-species discrete mutualism model with infinite deviating arguments: x1(k+1)=x1kexp⁡r1(K1+α1∑s=0+∞J2sx2k-s)/(1+∑s=0+∞J2sx2k-s)-x1k and  x2(k+1)=x2kexp⁡r2(K2+α2∑s=0+∞J1sx1k-s)/(1+∑s=0+∞J1sx1k-s)-x2k, where ri,Ki,αi, i=1,2, are all positive constants, ∑j=1+∞Ji(n)=1, and αi>Ki. Our results generalize the main result of Yang et al. (2014)

Stability and bifurcation in a Holling type II predator–prey model with Allee effect and time delay

Abstract In this paper, we consider a Holling type II predator–prey model incorporating time delay and Allee effect in prey. We discuss the influence of Allee effect on the logistic equation. By analyzing the characteristic equation of the corresponding linearized system, we give the threshold condition for the local asymptotic stability of the system according to the change of birth rate or Allee effect in prey. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. In addition, we show that if the Allee effect is large or the birth rate is small, then both predators and prey are extinct. The Allee effect can influence the stability of the system

Urinary biomonitoring of occupational exposures to Bisphenol A Diglycidyl Ether (BADGE) – based epoxy resins among construction painters in metal structure coating

Epoxy resin systems based on Bisphenol A Diglycidyl Ether (BADGE) monomer and its higher oligomers are important commercial formulations used widely in construction for protective coating of steel structures, such as bridges. The literature on occupational exposures and biomonitoring of BADGE-based epoxies among construction painters is remarkably limited. In this first occupational biomonitoring study of epoxies, 44 construction painters performing mid- and top-coating were recruited from 12 metal structure coating sites in New England. Cross-shift changes in the urinary levels of total BADGE and its three major hydrolysis derivatives - BADGE·2H2O, BADGE·H2O, BADGE·HCl·H2O – were assessed. Results for 81 urine samples collected from coating workers were compared with 28 urine samples of a reference group of 14 spray polyurethane foam (SPF) insulation workers.The highest concentrations of all biomarkers were found in the urine samples of mid-coat applicators. The major urinary biomarker of BADGE in this cohort of workers, BADGE·2H2O, was detected in 100% of urine samples. The post-shift BADGE·2H2O (specific gravity normalized data) in mid-coat applicators had a geometric mean (GM) of 1.46 ng/mL and a geometric standard deviation (GSD) of 3.6 (range, 0.2–18.7 ng/mL). The second most abundant biomarker in urine, BADGE·HCl·H2O, was measured in 84% of samples, and had a post-shift GM(GSD) of 0.17 (2.3) ng/mL (range, <0.025–0.59 ng/mL). BADGE·2H2O was 8.6 times more abundant than BADGE·HCl·H2O. BADGE·H2O was quantified only in 10% of the samples (range, 0.11–0.41 ng/mL). Free BADGE in post-shift urine, corrected for background, had GM (GSD) of 0.04 (2.5) ng/mL (range, <0.025–0.16 ng/mL). Urinary BADGE·2H2O were significantly higher (p = 0.01) in mid-coat applicators compared to top-coat and SPF workers. Post-shift urinary BADGE·2H2O in mid-coat applicators increased by ~2.9× (p = 0.02) and 1.36× in top-coat applicators (p = 0.18) compared to pre-shift values, but not in SPF workers (0.95×; p = 0.40).In conclusion, we demonstrate that (i) significant BADGE uptake occurs via inhalation and skin exposures during application of epoxy-containing paintings (mid-coat), suggesting the need for improvements in hygiene practices and personal protective measures; (ii) BADGE·2H2O is a robust and sensitive biomarker for biomonitoring of exposures to BADGE-based epoxies in occupational settings; and (iii) widespread occurrence of BADGE and BADGE·2H2O in the urine of all workers, including SPF workers, suggest common exposures from non-occupational sources, such as ingestion or do-it-yourself consumer applications of epoxy resins. In light of this observation, establishing a reliable biological monitoring guidance value (BMGV) for BADGE·2H2O will require more background biomonitoring and health effect data. An initial reference value for BADGE·2H2O of 0.5 ng/mL (SG-normalized) or 180 nmol/mol creatinine is being proposed as the threshold to discriminate occupational from non-occupational exposures based on the maximum values observed in the reference SPF group

Almost periodic solutions of a commensalism system with Michaelis-Menten type harvesting on time scales

In this paper, we consider an almost periodic commensal symbiosis model with nonlinear harvesting on time scales. We establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. Our results show that the continuous system and discrete system can be unify well. Examples and their numerical simulations are carried out to illustrate the feasibility of our main results

Note on the Stability Property of a Cooperative System Incorporating Harvesting

The stability of a kind of cooperative model incorporating harvesting is revisited in this paper. By using an iterative method, the global attractivity of the interior equilibrium point of the system is investigated. We show that the condition which ensures the existence of a unique positive equilibrium is enough to ensure the global attractivity of the positive equilibrium. Our results significantly improve the corresponding results of Wei and Li (2013)

Dynamic behaviors of a Lotka–Volterra commensal symbiosis model with density dependent birth rate

Abstract A Lotka–Volterra commensal symbiosis model with density dependent birth rate that takes the form dxdt=x(b11b12+b13x−b14−a11x+a12y),dydt=y(b21b22+b23y−b24−a22y), $$\begin{aligned} &\frac{dx}{dt}=x \biggl( \frac{b_{11}}{b_{12}+b_{13}x}-b_{14}-a_{11}x+a_{12}y \biggr), \\ &\frac{dy}{dt}=y \biggl( \frac{b_{21}}{b_{22}+b_{23}y}-b_{24}-a_{22}y \biggr), \end{aligned}$$ where bij $b_{ij}$, i=1,2 $i=1, 2$, j=1,2,3,4 $j=1, 2, 3, 4$, a11 $a_{11}$, a12 $a_{12}$, and a22 $a_{22}$ are all positive constants, is proposed and studied in this paper. The system may admit four nonnegative equilibria. By constructing some suitable Lyapunov functions, we show that under some suitable assumptions, all of the four equilibria may be globally asymptotically stable, such a property is quite different to the traditional Lotka–Volterra commensalism model. With introduction of the density dependent birth rate, the dynamic behaviors of the commensalism model become complicated