一类基于不同频率喷洒杀虫剂与投放染病害虫的害虫治理模型的研究

假设害虫种群分为易感害虫和染病害虫,运用分段连续的负指数函数模拟杀虫剂的作用方式,同时考虑到重复使用同一种化学杀虫剂,易感害虫会产生较强的抗药性,建立了一个杀虫剂喷洒比染病害虫投放更频繁的易感害虫产生抗药性的害虫治理模型,得到易感害虫根除周期解全局吸引的充分条件.数值模拟结果进一步表明易感害虫根除的阈值条件与杀虫剂喷洒的频率有关,最后确定了使易感害虫根除的染病害虫的投放量.     

具有饱和反应率和阶段时滞结构的害虫生物防治模型

考虑了一个害虫和天敌都有阶段结构及具有饱和反应率的阶段时滞脉冲捕食者-食饵模型,利用人工周期定量地投放有病的害虫和天敌去治理害虫.借助脉冲时滞微分方程的相关理论和方法获得易感害虫根除周期解全局吸引的充分条件以及天敌与易感害虫可以共存且易感害虫的密度可以控制在经济危害水平之下的充分条件.我们的结论为现实的害虫管理提供了可靠的策略依据.     

害虫管理策略的数学模拟

研究一类食饵(害虫)具有阶段结构并带有流行病、捕食者(天敌)具脉冲放养和时滞的捕食-食饵模型,得到了害虫灭绝周期解全局吸引的充分条件,以及当脉冲周期在一定范围内,易感害虫种群的密度可以控制在经济危害水平E(EIL)之下.所得结论将为现实的害虫管理提供一定的理论依据,数值分析也进一步说明系统的动力学性质.     

基于脉冲控制的害虫管理数学模型研究

研究一类害虫管理SI传染病模型,考虑脉冲投放病虫和人工捕杀相结合,得到系统的灭绝周期解,给出此周期解的全局吸引性,并获得了系统一致持续生存的条件.给出了害虫管理综合防治策略.     

食饵具有流行病的阶段结构捕食模型

本文考虑了一类食饵具有流行病和阶段结构的脉冲时滞捕食模型．利用脉冲时滞微分方程的相关理论和方法，获得易感害虫根除周期解全局吸引的充分条件以及当脉冲周期在一定范围内时，天敌与易感害虫可以共存且易感害虫的密度可以控制在经济危害水平E（EIL）之下．我们的结论为现实的害虫管理提供了可靠的策略依据．     

具有Monod-Haldane功能反应和脉冲效应的捕食系统的动力学性质

基于综合害虫防治,对具脉冲效应的Monod—Haldane功能反应的捕食系统进行了分析,根据Floquet乘子理论,获得了害虫灭绝周期解全局渐近稳定与系统持续生存的条件．并讨论了害虫灭绝周期解附近分支出非平凡周期解的问题,且文章利用Matlab软件对害虫灭绝周期解害虫周期爆发现象进行了数值模拟．     

捕食者具脉冲扰动与相互干扰的阶段结构时滞捕食-食饵模型

讨论了与害虫管理相关的一类捕食者具脉冲扰动与相互干扰的阶段结构时滞捕食-食饵模型,得到了害虫灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.我们的结论为现实的害虫管理提供了一定的理论依据.     

基于喷洒杀虫剂及释放病虫的脉冲控制害虫模型

基于喷洒杀虫剂及释放病虫的综合控制害虫策略,建立了具有脉冲控制的微分方程模型.利用脉冲微分方程的F loquet理论、比较定理,证明了害虫灭绝周期解的全局渐近稳定性与系统的持久性.     

捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型

讨论了与害虫治理相关的一类捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型,得到了害虫灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界．得出的结论为现实的害虫治理提供了可靠的策略依据．     

一类具有脉冲效应的食饵依赖捕食系统分析

基于害虫防治,该文提出了一类具有脉冲效应的食饵依赖捕食系统并进行了分析,根据Floquet乘子理论,我们获得了害虫根除周期解全局渐近稳定与系统持续生存条件.     

A deterministic algorithm for global optimization

We present an algorithm for finding the global maximum of a multimodal, multivariate function for which derivatives are available. The algorithm assumes a bound on the second derivatives of the function and uses this to construct an upper envelope. Successive function evaluations lower this envelope until the value of the global maximum is known to the required degree of accuracy. The algorithm has been implemented in RATFOR and execution times for standard test functions are presented at the end of the paper.Partially supported by NSF DMS-8718362.     

The minimal criterion for the equivalence between local and global optimal solutions in nondifferentiable optimization problem

In the paper, a necessary and sufficient criterion it provided such that any local optimal solution is also global in a not necessarily differentiable constrained optimization problem. This criterion is compared to others earlier appeared in the literature, which are sufficient but not necessary for a local optimal solution to be global. The importance of the established criterion is illustrated by suitable examples of nonconvex optimization problems presented in the paper.     

New Modified Function Method for Global Optimization

In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as the starting point, we obtain a better local optimal solution. This process is continued iteratively. A termination rule is obtained which can serve as stopping criterion for the iterating process. To demonstrate the efficiency of the proposed approach, numerical examples are solved.This research was partially supported by the National Science Foundation of China, Grant 10271073.     

A Free Boundary Problem of a Semilinear Combustible System with Higher Dimension and Heterogeneous Environment

In this paper, we investigate a free boundary problem of a semilinear combustible system with higher dimension and heterogeneous environment. Such a problem is usually used as a model to describe heat propagation in a two-component combustible mixture in which the free boundary is described by Stefan-like condition. For simplicity, we assume that the environment and solutions are radially symmetric. We use the contraction mapping theorem to prove the local existence and uniqueness of the solution. Also we study the blowup property and the long time behavior of the solution. Our results show that when pq › 1 blowup occurs if the initial datum is large enough and the solution is global and slow, whose decay rate is at most polynomial if the initial value is suitably large, while when p › 1, q › 1 there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small.     

Globally convergent algorithm for solving nonlinear equations

A general iterative method is proposed for finding the maximal rootx _max of a one-variable equation in a given interval. The method generates a monotone-decreasing sequence of points converging tox _max or demonstrates the nonexistence of a real root. It is globally convergent. A concrete realization of the general algorithm is also given and is shown to be locally quadratically convergent. Computational experience obtained for eight test problems indicates that the new method is comparable to known methods claiming global convergence.     

Global attractor for a density-dependent sensitivity chemotaxis model

In this paper, a chemotaxi model with reproduction term in a bounded domain Ω ⊂ Rⁿ is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.     

求解带箱子集约束的非光滑全局优化问题的填充函数方法

提出了一个求解带箱子集约束的非光滑全局优化问题的填充函数方法.构造的填充函数只包含一个参数,且此参数在迭代过程中容易调节.分析了填充函数的理论性质,在此基础上设计了填充函数算法.数值计算验证了该算法的有效性.     

全局优化问题的一个无参数填充函数算法

填充函数法是求解全局优化问题的一种有效的确定性算法,方法的关键在于填充函数的构造.对于一般无约束优化问题提出了一个新的无参数填充函数,通过定义证明了此填充函数能保持填充性质.利用其理论性质设计了相应的算法并对几个经典的算例进行了数值实验,实验结果表明算法有效可行.     

Blowup,Global Fast and Slow Solutions for a Semilinear Combustible System

In this paper, we investigate a semilinear combustible system $u_t-du_{xx}=v^p, v_t-dv_{xx}=u^q$ with double fronts free boundary, where p ≥ 1, q ≥ 1. For such a problem, we use the contraction mapping theorem to prove the local existence and uniqueness of the solution. Also we study the blowup and global existence property of the solution. Our results show that when pq › 1 blowup occurs if the initial datum is large enough and the solution is global and slow, whose decay rate is at most polynomial if the initial value is suitably large, while when p › 1, q › 1 there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small.