A ratio-dependent food chain model and its applications to biological control

While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics. Two trophic level Michaelis-Menten type ratio-dependent predator-prey system was globally and systematically analyzed in details recently. A distinct and realistic feature of ratio-dependence is its capability of producing the extinction of prey species, and hence the collapse of the system. Another distinctive feature of this model is that its dynamical outcomes may depend on initial populations levels. Theses features, if preserved in a three trophic food chain model, make it appealing for modelling certain biological control processes (where prey is a plant species, middle predator as a pest, and top predator as a biological control agent) where the simultaneous extinctions of pest and control agent is the hallmark of their successes and are usually dependent on the amount of control agent. Our results indicate that this extinction dynamics and sensitivity to initial population levels are not only preserved, but also enriched in the three trophic level food chain model. Specifically, we provide partial answers to questions such as: under what scenarios a potential biological control may be successful, and when it may fail. We also study the questions such as what conditions ensure the coexistence of all the three species in the forms of a stable steady state and limit cycle, respectively. A multiple attractor scenario is found.     

Numerical indices applied to the results of a survey of the macro-invertebrate fauna ofthe Tamar catchment (southwest England)

A survey ofthe macro-invertebrate fauna in the River Tamar revealed that a division ofthe catchment can be made which separates an organically enriched upper region from a more stable environment in the lower tributaries and reaches. Invertebrate species normally associated with organic pollution were found immediately downstream from farm waste and sewage effluent outfalls. Invertebrate species normally associated with an unpolluted condition were widely distributed throughout the catchment, and revealed that the Tamar is essentially free from gross pollution causing the continuous elimination of stream fauna. Systems used by pollution control organizations to codify biological results are reviewed and applied comparatively to the results. The Diversity index was found to be the most consistent method in assessing the biological state of the river. The Trent, Lothian, Chandler and Carpenter indices were found to give either anomalous figures or proved insensitive to conditions beyond a certain quality.     

基于“源-汇”景观的典型半城市化小流域非点源污染风险评价

小流域的水质恶化主要由点源污染和非点源污染引起,随着点源污染控制水平达到一定程度后,非点源污染已成为首要污染源。当前对非点源污染的管控仍存在难监测和难治理的问题,明晰非点源污染发生风险以及背后的原因是亟需解决的问题,因此开展非点源污染风险分析和评价具有重要意义。采用高分辨率影像解译了2010年、2015年和2020年三期厦门市后溪流域土地利用数据;基于"源-汇"景观格局方法计算研究区网格单元的网格污染指数（GPI）;结合土地利用变化数据分析非点源污染风险的时空变异,对风险区成因进行了分析。研究结果表明：当前,"汇"景观占流域面积的67.86%,非点源污染发生风险分布呈现北低南高;十年中,非点源污染风险呈现上升趋势,目前非点源污染发生风险处于低风险水平（GPI=0.27）。通过分析风险区的土地利用构成发现耕地面积的缩减（减少67.08%）和建设用地面积扩张（增加43.02%）是污染风险发生变动的主要原因。计算了风险区转移矩阵,发现非点源污染发生风险区呈现出中高风险区向低风险区和"汇"景观区域转移的趋势。基于"源-汇"景观格局理论计算的网格污染指数（GPI）可以有效地对流域非点源污染风险值进行表征,是评价和分析流域非点源污染发生风险的可用方法。     

Analyzing the mutual feedbacks between lake pollution and human behaviour in a mathematical social-ecological model

Does the adoption of environment-oriented actions by individuals necessarily improve the state of an ecosystem in the most effective way? We address this question with the example of eutrophication in shallow lakes. When exposed to fertilizers, such lakes can undergo a critical transition called eutrophication, resulting in a loss of biodiversity and ecosystem services. We couple a generic model of eutrophication with a best-response model of human behaviour, where agents can choose to pollute the lake at a high level (defection) or at a low level (cooperation). It is known that feedbacks between the interacting lake pollution and human behaviour can give rise to complex dynamics with multiple stable states and oscillations. Here, we analyze the impact of all model parameters on the shape of the nullclines. S-shaped nullclines are a condition for complex dynamics to occur. Moreover, we find that agents decreasing their pollution discharge into the lake is not necessarily the most effective way to reduce the pollution level in the lake. This is due to coexisting counterintuitive stable equilibria where the lake is in a clear state despite a high level of pollution discharge. We analyze the complex dynamics of the system and describe in detail Hopf, saddle-node, homoclinic and Bogdanov-Takens bifurcations. The complex dynamics with potential multistability and counterintuitive equilibria suggests that generic management recommendations holding for every level of pollution and of cooperation are impossible. Apart from the direct perturbation of an ecological variable, we identify three ways a management strategy can influence the social-ecological system: it can change the location, the resilience and the existence of stable equilibria.     

支气管哮喘患者疾病认知状况调查及控制水平的影响因素分析

目的:调查支气管哮喘患者疾病认知状况,并分析控制水平的影响因素。方法:选取2018年7月~2020年7月期间贵州医科大学附属医院诊治的支气管哮喘患者100例,采用面对面问卷调查的方式调查所有患者疾病认知状况。采用哮喘控制测试(ACT)对患者哮喘控制水平进行评估。根据ACT结果将患者分为哮喘未控制组(n=57)和哮喘控制组(n=43)。分析哮喘控制水平的影响因素。结果:支气管哮喘患者对疾病认知相关问题的回答正确率均在60%以上,但仅有12%的患者使用过峰流速仪。本研究中100例患者均完成ACT,其中完全控制17例,控制良好26例,未控制57例,分别占比17.00%、26.00%、57.00%,哮喘控制率为43.00%。由单因素分析显示,支气管哮喘患者的哮喘控制水平与性别、家庭月收入、文化程度、家族史、吸烟史、居住处是否空气污染、病程、哮喘用药依从性、使用吸入性糖皮质激素治疗、抑郁情况、焦虑情况有关(P<0.05)。多因素Logistic回归分析显示:焦虑情况、抑郁情况、居住处空气污染、吸烟史是支气管哮喘患者哮喘控制水平的危险因素,而哮喘用药依从性、使用吸入性糖皮质激素治疗是支气管哮喘患者哮喘控制水平的保护因素(P<0.05)。结论:支气管哮喘患者对疾病有一定的正确认知,但仍未达到理想状态。哮喘控制水平受多种因素影响,可根据相关影响因素做出针对性的干预措施,以改善支气管哮喘控制水平。     

Monitoring in a Lotka-Volterra model

The problem of monitoring arises when in an ecosystem, in particular in a system of several populations, observing some components, we want to recover the state of the whole system as a function of time. Due to the difficulty to construct exactly this state process, we look for an auxiliary system called an observer. This system reproduces this process with a certain approximation. This means that the solution of the observer tends to that of the original system. An important concept for this work is observability. This means that from the observation it is possible to recover uniquely the state process, however, without determining a constructive method to obtain it. If observability holds for the original system, it guarantees the existence of an auxiliary matrix that makes it possible to construct an observer of the system. The considered system of populations is described by the classical Lotka-Volterra model with one predator and two preys and the construction of its observer is illustrated with a numerical example. Finally, it is shown how the observer can be used for the estimation of the level of an abiotic effect on the population system.     

The coupled dynamics of human socio-economic choice and lake water system: the interaction of two sources of nonlinearity

We study a mathematical model for the coupled dynamics of human socio-economic choice and lake water system. In the model, many players choose one of the two options: a cooperative and costly option with low phosphorus discharge, and an economical option with high phosphorus discharge. The choice is affected by an economic cost, a social concern about water pollution, and a conformist tendency. The pollution level in the lake is determined by total phosphorus discharge by the players, the sedimentation and the outflow of phosphorus, and the recycling of phosphorus from the sediment. The model has two sources of nonlinearity: the cooperation level tends to be bistable due to conformist tendency of people (social hysteresis) and pollution level tends to be bistable because phosphorus recycling occurs faster in more eutrophic lakes (ecological hysteresis). The combination of these two sources may cause multiple stable equilibria or oscillations with a long periodicity. Small economic cost and strong social concern about pollution level can decrease the pollution level, but may not be very effective in enhancing the cooperation level. In contrast, strong conformist tendency produces a stable state with a high cooperation level and a low pollution level. We discuss implications of these results to the water quality management.     

Metabolism analysis and on-line physiological state diagnosis of acetone-butanol fermentation

Fermentation equations for acetone-butanol (AB) were applied in a metabolic analysis of the reaction network under various conditions; that is, at different pHs and a high NADH2 turnover rate using methyl viologen, in a Clostridium acetobutylicum culture. The results disclosed variations in the pattern of rate changes that reflected changes in the physiological state. A linear relationship was found to exist between NADH2 generation and butanol production rate. By coupling an automated measurement system with the fermentation model, on-line estimation of the culture state was accomplished. Based on the AB fermentation model, new parameters were defined for on-line diagnosis of the physiological state and determination of the best timing for amplifying NADH2 generation by the addition of methyl viologen to obtain a high level of butanol productivity. A potential means of achieving optimal control for a high level of solvent production, involving the correlation of certain rates, is proposed.     

An optimizing start-up strategy for a bio-methanator

This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang–bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.     

Identifying the spatial effects and driving factors of urban PM2.5 pollution in China

Exploring exactly where air pollution comes from, and identifying the key factors that influence it, can provide a scientific basis for the rational formulation and effective implementation of air pollution policies in China. Based on the data from 2001 to 2012 covering PM_2.5 concentrations in 285 Chinese cities, we use dynamic spatial panel models to empirically analyze the key driving factors of this air pollution. Results show that China’s urban smog demonstrates both obvious global spatial autocorrelation and local spatial agglomeration. There is a significant inverted “U-shaped” curve between economic development level and air pollution, and most cities are in the phase in which pollution is increasing in conjunction with improvements to the economy. Due to a rapid increase in population in built up areas, a high-proportion of secondary industry, a coal-dominated energy structure and increasing traffic intensity, China’s smog problem is becoming more and more serious. FDI probably will not play a future role in mitigating the air pollution. Central heating in winter in northern China further aggravates local smog to a certain extent. Because China’s haze pollution presents path-dependent characteristics and spatial spillover effects in the time dimension and in the space dimension respectively, so smog alleviation policies should be implemented based both on the strategies of maximizing effort and regional joint prevention and control.     

Monitoring environmental change in an ecosystem

The monitoring and analysis of the processes taking place in an ecosystem is a key issue for a sustainable human activity. A system of populations, as the biotic component of a complex ecosystem is usually affected by the variation of its abiotic environment. Even in nearly natural ecosystems an abiotic effect like climatic implications of global warming may cause important changes in the dynamics of the population system. In ecosystems involving field cultivation or any industrial activity; the abiotic parameter in question may be the concentration of a substance, changing, e.g. as a result of pollution, application of a pesticide, or a fertilizer, etc. In many cases the observation of the densities of each population may be technically complicated or expensive, therefore the question arises whether from the observation of the densities of certain (indicator) populations, the whole state process of the population system can be uniquely recovered. The paper is aimed at a methodological development of the state monitoring, under the conditions of a changing environment. It is shown, how the technique of mathematical systems theory can be applied not only for the approximate calculation of the state process on the basis of the observed data, even under the effect of an exogene abiotic change with known dynamics; but in certain cases, also for the estimation of the unknown biological effect of the change of an abiotic parameter. The proposed methodology is applied to simple illustrative examples concerning a three-species predator-prey system.     

Trophic state, eutrophication and nutrient criteria in streams

Trophic state is the property of energy availability to the food web and defines the foundation of community integrity and ecosystem function. Describing trophic state in streams requires a stoichiometric (nutrient ratio) approach because carbon input rates are linked to nitrogen and phosphorus supply rates. Light determines the source of carbon. Cross system analyses, small experiments and ecosystem level manipulations have recently advanced knowledge about these linkages, but not to the point of building complex predictive models that predict all effects of nutrient pollution. Species diversity could indicate the natural distribution of stream trophic status over evolutionary time scales. Delineation of factors that control trophic state and relationships with biological community properties allows determination of goals for management of stream biotic integrity.     

Design Guidelines for Deadlock-Handling Strategies in Flexible Manufacturing Systems

Deadlock-free operation of flexible manufacturing systems (FMSs) is an important goal of manufacturing systems control research. In this work, we develop the criteria that real-time FMS deadlock-handling strategies must satisfy. These criteria are based on a digraph representation of the FMS state space. Control policies for deadlock-free operation are characterized as partitioning cuts on this digraph. We call these structural control policies (SCPs) because, to avoid deadlock, they must guarantee certain structural properties of the subdigraph containing the empty state; namely, that it is strongly connected. A policy providing this guarantee is referred to as correct. Furthermore, an SCP must be configurable and scalable; that is, its correctness must not depend on configuration-specific system characteristics and it must remain computationally tractable as the FMS grows in size. Finally, an SCP must be efficient; that is, it must not overly constrain FMS operation. We formally develop and define these criteria, formulate guidelines for developing policies satisfying these criteria, and then provide an example SCP development using these guidelines. Finally, we present an SCP that guarantees deadlock-free buffer space allocation for FMSs with no route restrictions.     

Regulation of the organic pollution level in anaerobic digesters by using off-line COD measurements

A sampled delayed scheme is proposed to regulate the organic pollution level in anaerobic digestion processes by using off-line COD measurements. The proposed scheme is obtained by combining an error feedback control with a steady state estimator to track constant references and attenuate process load disturbances. The controller performance is tested experimentally for the treatment of tequila vinasses over a period of 68 days under different set-point values and several uncertain scenarios which include badly known kinetic parameters and load disturbances. Experimental results show that the COD concentration can be effectively regulated under the influence of set-point changes and high load disturbances by using only a daily off-line COD measurement, which makes the industrial application of the proposed control scheme feasible.     

线性广义系统的无源控制

研究线性广义系统在有界能量外部输入作用下的无源控制问题,给出广义系统容许且具有严格无源性的充分条件,并且在一定条件下设计一个状态反馈控制器使得闭环系统容许,同时具有严格无源性．     

Ecological ranging of the Volgograd territory on the basis of Staphylococcus aureus resident carrier state determination

The evaluation of S. aureus resident carrier state on the nasal mucosa among school children showed that its intensity was determined by the ecological factors in the place of residence. Under favorable conditions of the central part of the city the level of S. aureus carrier state was 25.4 +/- 3.1%, while in the northern and southern parts of the city, where most of major metallurgical and chemical plants are situated, these values were 44.4 +/- 4.2% and 45.9 +/- 1.6%. The calculation of the factor of staphylococcal resident carrier state (FSRCS), i.e. the ratio of the carrier state levels in the ecologically favorable (control) zone and in the zone under study, revealed that the FSRCS values in the northern and southern zones were 1.81 and 1.74. Thus the ecological situation could be regarded as critical in none of the districts of Volgograd. The levels of S. aureus resident carrier state were highly correlated to the degree of air pollution, evaluated by the factor of total air pollution, and upper respiratory tract diseases in children. The level of S. aureus resident carrier state may be used as a marker in the ecological ranging of the city territories.     

Pollution and parasitism in the aquatic environment

The studies of aquatic parasitology and of aquatic pollution effects both have experienced increasing interest during the recent fifteen years. Although considerable effort has been spent on studying the role of pollution as a cause or a trigger of anomalies, tumors and infectious diseases in aquatic organisms, the interactions between pollution and parasitism have been largely neglected by scientists.Pollution and other man-made alterations of the aquatic environment may affect a parasite community directly by acting on free-living parasite stages or on ectoparasites, or indirectly by acting on the intermediate or the definitive host population. Certain pollution conditions favour the propagation of parasites by excluding their natural predators, by reducing the resistance of their hosts or by providing improved living conditions for their intermediate hosts. In a number of experimental studies parasitized organisms have been shown to suffer from greater mortalities when exposed to high temperature, to low oxygen stress or to high levels of dissolved heavy metal salts, when compared to nonparasitized control animals. Unfortunately, field studies on synergistic effects of pollution and parasites on host populations are still scarce and seldom offer more than qualitative observations and theoretical evaluations.The complexity of the pollution-parasite-host system complicates the use of parasites as indicators of pollution effects. However, experience from aquaculture practice teaches that a number of (mostly ecto-) parasites are more susceptible to certain chemicals (used as parasiticides) and to artificial alterations of salinity, temperature or oxygen content of the water than their hosts. Accordingly, it is postulated that during future studies the composition of ectoparasitic faunas of aquatic organisms might turn out to become a useful and quickly reacting indicator for effects of certain pollution conditions, such as anthropogene oxygen deficiency, salt introduction from salines into freshwater ecosystems, and introduction of certain heavy metal salts.     

Derivation of dynamic reference values for the classification of contaminant concentrations in bream (Abramis brama) of German rivers and lakes using data of the Environmental Specimen Bank

A direct assessment of contaminant concentrations in biota with respect to their biological relevance or importance for the ecosystem is rarely possible. Statistically derived reference values can serve as a guide to classify measured tissue concentrations, but they do not provide any information on the biological significance of the contaminant concentrations. However, previously such reference values did not exist for environmental-biomonitoring. Based on analytical data from muscle tissue of bream (Abramis brama) of the German Environmental Specimen Bank (ESB), we present a method on how to derive dynamic reference values. These show the general state of inland surface water pollution in Germany at a certain time. The reference values allow for classification of measured contaminant concentrations in muscle tissue of bream. This classification enables a comparative assessment in means of how the actual state of pollution in a specific ecosystem is, compared to the general, macro state of pollution.     

Structure of the crown of Siberian larch as a complex stability index of trees in the plantations of Krasnoyarsk

The state of larch plantations has been analyzed in residential districts of Krasnoyarsk differing in the level of air pollution. The crown structure is characterized and correlations are established between the habit signature and tree states observed in the regions with medium and high levels of air pollution. It is concluded that the sensitivity of correlation signs is high enough to reveal the changes in tree state that cannot be diagnosed by eye.