带时变增长率、迁移率、波动率的种群变动模型与生物防治最小成本的确定方法

用回归方法确定种群数量增长率、迁移率与波动率的最优拟合曲线,求解带时变漂移串与波动串的It(?)随机微分方程,建立有迁移行为的害虫种群的数量变动模型,进而给出确定生物防治最小成本的计算方法,指出了确定模型中参数的统计方法。     

一类带有一般出生率的SIS传染病模型的全局分析

将一般出生率系数引入S IS传染病模型,得到了种群灭绝和疾病灭绝的阈值条件.分别借助S tokes定理和D u lac函数对染病者的数量模型和染病者在种群中所占比例的模型进行了讨论,得到了相应模型的全局动力学行为.     

具阶段结构害虫防治模型的脉冲效应

对于用微分方程描述的种群生态动力系统，其研究结果已十分丰富，但自然界中的许多变化规律都呈现出脉冲效应，因此用脉冲微分方程描述某些运动状态在固定或不固定时刻的快速变化或跳跃更切合实际，尤其在刻画种群生长和流行病动力学行为方面，脉冲微分方程的描述显得更科学更真实，具有脉冲效应的种群动力学模型的研究目前还处于刚刚起步阶段，本对符合实际的有脉冲效应的具阶段结构的常系数害早防治模型进行了研究，得到了系统存在周期解的充分条件，系统存在唯一周期解的充分条件，系统周期解轨道渐近稳定的充分条件。     

两类两种群动力学方程的稳定性分析

本文研究两种群动力学方程平衡点的稳定性.讨论两个捕食者-食饵-领地模型,模型用1微分方程描述,模型2用积分微分方程描述.得出平衡点稳定的条件.所得结果指出可实现总体的种群稳定而不管局部的绝灭.     

含参数泛函微分方程概周期正解的存在性

研究了一类含参数泛函微分方程概周期正解的存在性问题.结合有界性及渐近概周期性获得了系统存在概周期正解的几组充分条件,并将结果应用于几类种群动力学模型,分别获得了系统在概周期环境下存在概周期解的一组充分条件.     

毒素脉冲输入与种群脉冲出生切换阶段结构单种群动力学模型研究

本文研究了毒素脉冲输入与脉冲出生切换阶段结构单种群动力学模型.利用常微分方程及差分分析,获得了系统种群灭绝和持久生存的控制条件结果,为污染环境中的生物资源管理提供了可靠的管理策略.     

污染喀斯特环境下具瞬时与非瞬时脉冲效应的单种群动力学模型

建立污染喀斯特环境下具瞬时与非瞬时脉冲效应的单种群动力学模型.利用脉冲微分方程理论,得到系统种群持续生存的控制阈值.研究结果表明瞬时脉冲收获量与非瞬时脉冲收获区间长度对于系统种群持久起着重要作用,结论为现实的生物资源管理提供了可靠的策略支持.     

具脉冲效应的阶段结构单种群动力学模型

讨论了生物资源管理中的具脉冲出生与脉冲收获的单种群阶段结构动力学模型.利用离散动力系统频闪映射理论,得到了脉冲投放幼体对整个种群持续生存的重要意义.为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲微分方程理论.     

一阶多参数模糊微分方程及定解问题

在单参数模糊微分方程基础上研究了一阶多参数模糊微分方程和模糊初值问题,利用刻画方程的解与刻画参数的关系给出了多参数模糊微分方程解存在的条件,最后给出了具体算例.表明,多参数模糊微分方程具有广泛的工程应用背景.     

径流中长期预报模糊识别优化模型及应用

对水文中长期预报模糊识别方法进一步研究,基于模糊环境下的目标函数,提出了具有主观监督因子和稳定系数的模糊识别预报模型.根据已知样本的最优模糊划分建立预报模型,利用已知样本的指标和样本的最优模糊划分计算预报模型的参数,给定模型的稳定系数,再通过调整主观监督因子对预报模型参数进行优化.径流中长期预报实例的模型检验平均相对误差为7.84%.     

比类型估计量在数量特征随机化回答技术中的应用

本文在数量特征随机化回答技术中当变异系数、偏度系数、峰度系数已知时,对总体均值提出了一系列比类型估计量,并且在一定条件下,证明了这些估计量优于Gupta et al.提出的估计量。     

Estimation of more than one parameters in stratified sampling with fixed budget

In a multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. A compromise criterion is needed to work out a usable allocation which is optimum, in some sense, for all the characteristics. When auxiliary information is also available the precision of the estimates of the parameters can be increased by using it. Furthermore, if the travel cost within the strata to approach the units selected in the sample is significant the cost function remains no more linear. In this paper an attempt has been made to obtain a compromise allocation based on minimization of individual coefficients of variation of the estimates of various characteristics, using auxiliary information and a nonlinear cost function with fixed budget. A new compromise criterion is suggested. The problem is formulated as a multiobjective all integer nonlinear programming problem. A solution procedure is also developed using goal programming technique.     

Distribution estimation with smoothed auxiliary information

Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution.In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information,for example,a symmetric distribution of this variable.A smoothing technique is employed to handle the non-differentiable function.Hence,a distribution can be estimated based on smoothed auxiliary information.Asymptotic properties of the distribution estimator are derived and analyzed.The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information.Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.     

Bootstrap Algorithms for Risk Models with Auxiliary Variable and Complex Samples

Resampling methods are often invoked in risk modelling when the stability of estimators of model parameters has to be assessed. The accuracy of variance estimates is crucial since the operational risk management affects strategies, decisions and policies. However, auxiliary variables and the complexity of the sampling design are seldom taken into proper account in variance estimation. In this paper bootstrap algorithms for finite population sampling are proposed in presence of an auxiliary variable and of complex samples. Results from a simulation study exploring the empirical performance of some bootstrap algorithms are presented.      

Determining the Optimum Stratum Boundaries Using Mathematical Programming

The method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation, is known as optimum stratification. In order to make the strata internally homogeneous, the strata are constructed in such a way that the strata variances should be as small as possible for the characteristic under study. In this paper the problem of determining optimum strata boundaries (OSB) is discussed when strata are formed based on a single auxiliary variable with a varying measurement cost per units across strata. The auxiliary variable considered in the problem is a size variable that holds a common model for a whole population. The OSB are achieved effectively by assuming a suitable distribution of the auxiliary variable and creating strata by cutting the range of the distribution at optimum points. The problem of finding the OSB, which minimizes the variance of the estimated population mean under a weighted stratified balanced sampling, is formulated as a mathematical programming problem (MPP). Treating the formulated MPP as a multistage decision problem, a solution procedure using dynamic programming technique is developed. A numerical example using a hospital population data is presented to illustrate the computational details of the solution procedure. A software program coded in JAVA is written to carry out the computation. The distribution of the auxiliary variable in this example is considered to be continuous with an exponential density function.     

Multiscaling analysis of a slowly varying single species population model displaying an Allee effect

We consider the growth of a single species population modelled by a logistic equation modified to accommodate an Allee effect, in which the model parameters are slowly varying functions of time. We apply a multitiming technique to construct general approximate expressions for the evolving population in the case where the population survives to a (slowly varying) finite positive limiting state, and that where the population declines to extinction. We show that these expressions give excellent agreement with the results of numerical calculations for particular instances of the changing model parameters. Copyright © 2013 John Wiley & Sons, Ltd.     

The chaos and control of a food chain model supplying additional food to top-predator

The control and management of chaotic population is one of the main objectives for constructing mathematical model in ecology today. In this paper, we apply a technique of controlling chaotic predator–prey population dynamics by supplying additional food to top-predator. We formulate a three species predator–prey model supplying additional food to top-predator. Existence conditions and local stability criteria of equilibrium points are determined analytically. Persistence conditions for the system are derived. Global stability conditions of interior equilibrium point is calculated. Theoretical results are verified through numerical simulations. Phase diagram is presented for various quality and quantity of additional food. One parameter bifurcation analysis is done with respect to quality and quantity of additional food separately keeping one of them fixed. Using MATCONT package, we derive the bifurcation scenarios when both the parameters quality and quantity of additional food vary together. We predict the existence of Hopf point (H), limit point (LP) and branch point (BP) in the model for suitable supply of additional food. We have computed the regions of different dynamical behaviour in the quantity–quality parametric plane. From our study we conclude that chaotic population dynamics of predator prey system can be controlled to obtain regular population dynamics only by supplying additional food to top predator. This study is aimed to introduce a new non-chemical chaos control mechanism in a predator–prey system with the applications in fishery management and biological conservation of prey predator species.     

Harvesting a logistic population in a slowly varying environment

The classic problem for a logistically evolving single species population being harvested involves three parameters: rate constant, carrying capacity and harvesting rate, which are taken to be positive constants. However, in real world situations, these parameters may vary with time. This paper considers the situation where these vary on a time scale much longer than that intrinsic to the population evolution itself. Application of a multiple time scale approach gives approximate explicit closed form expressions for the changing population, that compare favorably with those generated from numerical solutions.     

Using a signature function to determine resonant and attenuant 2-cycles in the Smith–Slatkin population model

We study the responses of discretely reproducing populations to periodic fluctuations in three parameters: the carrying capacity and two demographic characteristics of the species. We prove that small 2-periodic fluctuations of the three parameters generate 2-cyclic oscillations of the population. We develop a signature function for predicting the responses of populations to 2-periodic fluctuations. Our signature function is the sign of a weighted sum of the relative strengths of the oscillations of the three parameters. Periodic environments are deleterious for populations when the signature function is negative, while positive signature functions signal favorable environments. We compute the signature function for the Smith–Slatkin model, and use it to determine regions in parameter space that are either favorable or detrimental to the species.