分布在非齐次空间中捕食－被捕食系统的锁相振动

本文以经典的带有时滞的捕食－被捕食系统为基础，构造了一类泛函微分方程作为描述分布在由ｎ个岛屿构成的环状区域上的捕食－被捕食种群生长过程的模型．我们假设种群在最相邻的岛屿间相互迁移，以迁移率为分支参数，研究了该系统的锁相振动，给出了离散波分支的存在条件．     

环状岛屿环境中捕食-食系统全局离散波分支

本文研究了一类用以描述分布在环状岛屿环境中的捕食-被捕食系统生长过程的泛函微分方程．假设所考虑的种群仅在最相邻的岛屿间相互迁移．得到了该系统存在全局离散波分支的充分条件．也称离散波为锁相振动．即每个岛屿上的种群数量呈周期性变化，而这种周期性振动彼此相似，但差一个相位．     

一类捕食与被捕食模型极限环的存在性

本文考虑一类被捕食种群为线性密度制约，捕食者种群无密度制约且具ＨｏｌｌｉｎｇⅠ型功能性反应的捕食与被捕食两种群模型　得到了系统存在极限环的必要条件，且证明了当ｂ充分小时，系统至少存在两个极限环。     

一类捕食者具有阶段结构的捕食——被捕食模型的全局性态分析

在假设捕食的受益是减少死亡下,建立了一类捕食种群具有阶段结构的捕食-被捕食模型,分析得到了不存在食饵种群情形下捕食者种群模型和食饵存在时捕食-被捕食模型的平衡点存在性和全局稳定性,并确定了决定模型动力学性态的捕食者种群基本再生数、捕食存在时的食饵种群净增长率以及食饵灭绝与否的捕食率阈值.     

周期捕食与被捕食系统正周期解的稳定性

本文研究具周期系数的Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ捕食与被捕食系统，建立了系统正周期解渐近稳定和全局稳定的新的判别准则。     

一类具有多时滞捕食－被捕食系统正周期解的存在性

研究一类具有多时滞Holling II型功能性反应非自治捕食－被捕食系统, 利用重合度理论得到系统全局正周期解存在的充分条件．推广了相关的已有结果．     

具有脉冲效应非自治捕食系统的研究

研究了具有脉冲效应的非自治捕食系统,该系统是两个具有互惠关系的食饵种群被一个捕食种群捕食.利用重合度理论证明系统正周期解的存在性.     

在容量较小的污染环境中二维捕食系统的持续生存与绝灭

利用极限理论及积分均值法研究了在容量较小的污染环境中毒素对二维Lotka-Volterra捕食被捕食系统持续生存与绝灭的影响,给出了捕食种群与食饵种群弱平均持续生存和绝灭的充分条件.     

一类具有Allee影响的捕食与被捕食模型

分析并建立了具有Allee影响的捕食与被捕食模型,被捕食者由于自身繁殖或是被捕食而具有了Allee效应,分别讨论了强Allee和弱Allee对被捕食种群的影响,讨论了解的有界性和各平衡点的存在性,并证明了各平衡点的局部渐近稳定性,进一步通过构造适当的Lyapunov函数分析了正平衡点E*的全局渐近稳定性.     

多种群生态竞争-捕食时滞系统正周期解的全局吸引性

本文利用比较定理结合Ｌｉａｐｕｎｏｖ泛函的方法，　讨论一类具有多个时滞的多种群生态竞争－捕食系统正周期解的存在性和全局吸引性，得到了一些新的结果，　并举例说明条件的可行性．     

Security protection design for deception and real system regimes: A model and analysis

In this paper, we model a possible deception system with the explicit purpose of enticing unauthorized users and restricting their access to the real system. The proposed model represents a system designer’s defensive actions against intruders in a way that maximizes the difference between the intruders’ cost and the system designer’s cost of system protection. Under the assumption of a dual entity system, the proposed model shows that intruders differ in behavior depending on the system’s vulnerability at the time of intrusion as well as depending on their own economic incentives. The optimal results of the proposed model provide the system designer with insights on how to configure the level of protection for the two systems.     

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part II: Nonlinear system simulation and control

As was stated in Part I, the linear control models of a radically rotating elastic rod in all the analysis and design procedures for lead with closed-loop system compensation is presented. For a given linear system model, if the model is accurate, it will be accurate only over a very limit range of operation of the system. However, all the effort of design comes to be meaningful until it is tested using the nonlinear system model. On the other hand, the response of the nonlinear system model will not be as good as that of the linear model. In fact, some iterations on the design and on improving the design based-model are often needed before there is even a resemblance between the linear model response and the nonlinear system response. The present paper is a continuation of [1] and nonlinear control system simulation and a tuning process are presented. While almost all design procedures for physical system contain some tuning process, the development of an analytic design procedure for models of distributed-parameter control system can be evidently shown through this paper.     

First Steps Towards an Institution of Algebra Replacement Systems

Algebra replacement systems are introduced as formal models of state dependent and state transforming systems. The first part of an institution of algebra replacement systems is developed, that is, a model theoretic and logical framework that can be used to describe and reason about such systems. The usual operational understanding of a replacement system as a labeled transition system is then considered as one particular model in the model category. Under appropriate conditions such a constructed replacement system is initial.     

Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting

A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, dynamic behavior of the proposed model system with and without discrete time delay is investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; Furthermore, local stability of the model system with discrete time delay is studied. It reveals that the discrete time delay has a destabilizing effect in the population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Finally, numerical simulations are carried out to show the consistency with theoretical analysis obtained in this paper.     

Ergodic dynamics of the coupled quasigeostrophic-flow-energy-balance system

The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic-flow-energy-balance model. This model consists of the large-scale quasigeostrophic oceanic flow model and the transport equation for oceanic temperature, coupled with an atmospheric energy-balance model. After reformulating this coupled model as a random dynamical system (cocycle property), it is shown that the coupled quasigeostrophic-energy balance fluid system has a random attractor, and under further conditions on the physical data and the covariance of the noise, the system is ergodic, namely, for any observable of the coupled atmosphere-ocean flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 67–84, 2006.     

Reliability and cost analysis of series system models using fuzzy parametric geometric programming

In this paper, we have discussed series system models with system reliability and cost. We have considered two types of the model; the former focuses on a problem of optimal reliability for series system with cost constraint and the latter is a center system cost model with reliability goal. It is necessary to improve the reliability of the system under limited available cost of system and also to minimize the systems cost subject to target goal of the reliability. Practically, cost of components has always been imprecise with vague in nature. So they are taken as fuzzy in nature and the reliability models are formulated as a fuzzy parametric geometric programming problem. Numerical examples are given to illustrate the model through fuzzy parametric geometric programming technique.     

Multi-Model Communication and Data Assimilation for Mitigating Model Error and Improving Forecasts

Models for weather and climate prediction are complex, and each model typi-cally has at least a small number of phenomena that are poorly represented, such as perhaps the Madden-Julian Oscillation (MJO for short) or El Ni\~{n}o-Southern Oscillation (ENSO for short) or sea ice. Furthermore, it is often a very challenging task to modify and improve a complex model without creating new deficiencies. On the other hand, it is sometimes possible to design a low-dimensional model for a particular phenomenon, such as the MJO or ENSO, with significant skill, although the model may not represent the dynamics of the full weather-climate system. Here a strategy is proposed to mitigate these model errors by taking advantage of each model''s strengths. The strategy involves inter-model data assimilation, during a forecast simulation, whereby models can exchange information in order to obtain more faithful representations of the full weather-climate system. As an initial investigation, the method is examined here using a simplified scenario of linear models, involving a system of stochastic partial differential equations (SPDEs for short) as an imperfect tropical climate model and stochastic differential equations (SDEs for short) as a low-dimensional model for the MJO. It is shown that the MJO prediction skill of the imperfect climate model can be enhanced to equal the predictive skill of the low-dimensional model. Such an approach could provide a route to improving global model forecasts in a minimally invasive way, with modifications to the prediction system but without modifying the complex global physical model itself.     

害虫综合防治建模驱动“半连续动力系统理论”兴起

以害虫综合防治数学建型为启迪,对生物数学研究的一些相关问题开展了一系列的研究.从实际问题出发,我们分别建立了"常微分方程模型"以及对应的"周期脉冲控制模型";随着害虫综合防治常态化管理和环境污染常态化防治的兴起,我们建立了"状态脉冲反馈控制系统"模型,简称"半连续动力系统"模型,提出了"半连续动力系统"相关的概念,创建了其基本理论,并且作了系统性的研究,例如:半连续动力系统的周期解以及周期解的稳定性、同宿轨和同宿分支、异宿轨和异宿分支以及"双边控制系统"等概念及其判定定理的研究;进一步将"半连续动力系统"相应的理论和方法应用于生物数学其他方面的一些相关问题的研究.本文以数学模型为载体,归纳总结了近十多年来对生物数学的研究历程,指出了当前研究中尚待解决的问题.     

Dynamic system optimal performances of shared autonomous and human vehicle system for heterogeneous travellers

ABSTRACT

Autonomous vehicles (AV) can solve vehicle relocation problems faced by traditional one-way vehicle-sharing systems. This paper explores the deterministic time-dependent system optimum of mixed shared AVs (SAV) and human vehicles (SHV) system to provide the benchmark for the situation of mixed vehicle flows. In such a system, the system planner determines vehicle-traveller assignment and optimal vehicle routing in transportation networks to serve predetermined travel demand of heterogeneous travellers. Due to large number of vehicles involved, travel time is considered endogenous with congestion. Using link transmission model (LTM) as a traffic flow model, the deterministic time-dependent system optimum is formulated as linear programming (LP) model to minimize the comprehensive cost including travellers’ travel time cost, waiting time cost and empty vehicle repositioning time cost. Numerical examples are conducted to show system performances and model effectiveness.     

An intelligent system for prioritisation of organ transplant patient waiting lists using fuzzy logic

The objective of this paper is to investigate the effectiveness of using fuzzy logic in a complex decision-making capacity, and in particular, for the prioritisation of kidney transplant recipients. Fuzzy logic is an extension to Boolean logic allowing an element to have degrees of true and false as opposed to being either 100% true or 100% false. Thus, it can account for the ‘shades of grey’ found in many real-world situations. In this paper, two fuzzy logic models are developed demonstrating its effectiveness as a model for vastly improving the current prioritisation system used in the UK and abroad. The first model converts an element of the current kidney transplant prioritisation system used in the UK into fuzzy logic. The result is an improvement to the current system and a demonstration of fuzzy logic as an effective decision-making approach. The second model offers an alternative prioritisation system to overcome the limitations of the current system both in the UK and abroad, as brought up by research reviewed in this paper. The current UK transplant prioritisation system, adapted in the first model, uses objective criteria (age of recipient, waiting time, etc) as inputs into the decision-making process. This alternative model takes advantage of the facility for infinitely varying inputs into fuzzy logic and a system is developed that can handle subjective (humanistic) criteria (pain level, quality of life, etc) that are key to arriving at such important decisions. Furthermore, the model is highly flexible allowing any number of criteria to be used and the individual characteristics of each criterion to be altered. The result is a model that utilises the scope of fuzzy logic's flexibility, usability and effectiveness in the field of decision-making and a transplant prioritisation method vastly superior to the original system, which is constrained by its use of only objective criteria. The ‘humanistic’ model demonstrates the ability of fuzzy logic to consider subjective and complex criteria. However, the criteria used are not intended to be exhaustive. It is simply a template to which medical professionals can apply limitless additional criteria. The model is produced as an alternative to any current national system. However, the model can also be used by individual hospitals to decide initially whether a patient should be placed on the transplant or surgery waiting list. The model can be further adapted and used for the transplant of other organs or similar decisions in medicine. Concurrently with the research and work carried out to develop the two models the investigation focused on the constraints of the current systems used in the UK and the US and the seemingly impossible dilemmas experienced by those having to make the prioritisation decisions. By removing the parameters of objective-only inputs the ‘humanistic’ model eradicates the previous limitations on decision-making.