随机数学中若干典型问题的计算机仿真

运用计算机代数系统Maple研究了随机数学中若干典型问题的计算机仿真．研究结果表明，计算机仿真是数学实验的重要手段之一，也是科学研究的重要方法．     

《实变函数与泛函分析》教学改革初探——以实数的三个性质到正算子的推广为例

以＂实数的三个性质到希尔伯特空间中正算子的推广＂为教学案例,探讨了《实变函数与泛函分析》的教学改革问题,提出＂由简单类比复杂＂的教学模式,这将为创新型人才培养提供参考.     

描述草地资源与草食动物分布的扩散模型Ⅲ

草地资源与资源利用者－草信动物的时、空格局及其保持和发展机制,以及对种和生态系统动态所生产的影响一直是草原生态２学研究的主要课题之一,也是草地农业生态学中一切问题的核心。针对草地上草食动物（家蓄）种群空间格局的三种主要类型;辐射型、带型和缀块型,利用随机过程、微分方程的理论和方法,研究了两个同类资源点之间的草地上草食动物的分布。建立了描述草地资源与草食动物时空分布的扩散模型,这类模型不仅可以通过极     

具有脉冲控制及扩散的Watt型食饵-捕食系统的周期解的存在性

对一类具有脉冲生育的Watt型捕食扩散系统,限制捕食者只能在一个斑块中活动,利用重合度理论得到了系统存在正周期解的充分条件.     

非自治耗散Schr\"odinger-Boussinesq 方程组紧致核截面的存在性$^$

讨论满足齐次Dirichlet边界条件的非自治耗散Schr\"odinger-Boussinesq 方程组解的长时间行为. 通过 对方程作适当的分解, 证明了方程组所生成的过程存在紧致核截面.     

Pattern selection in a predation model with self and cross diffusion

In this paper, we present the amplitude equations for the excited modes in a cross-diffusive predator--prey model with zero-flux boundary conditions. From these equations, the stability of patterns towards uniform and inhomogenous perturbations is determined. Furthermore, we present novel numerical evidence of six typical turing patterns, and find that the model dynamics exhibits complex pattern replications: for μ₁<μ≤μ₂, the steady state is the only stable solution of the model; for μ₂<μ≤μ₄, by increasing the control parameter μ, the sequence H_π-hexagons → H₀-hexagon-stripe mixtures rightarrow stripes → H_π-hexagon-stripe mixtures → H₀-hexagons is observed; for μ>μ₄, the stripe pattern emerges. This may enrich the pattern formation in the cross-diffusive predator--prey model.     

温州市区手足口病SARIMA模型建立及应用

基于温州市区(鹿城区、瓯海区、龙湾区)2011年1月至2017年12月月报手足口病新发病人数统计数据,构建了季节求和自回归-移动平均模型(SARIMA).结果表明SARIMA(2,1,1)(0,1,1)_([12])模型平均绝对百分误差(MAPE)为6.002%,能较好的拟合出温州市区手足口新发病人数的季节性和趋势性特征.在对拟合值进行指数化和周期性还原后,预测2018年1-6月温州市区手足口新发病人数仍维持较高水平,其中6月份达到最高1094 (95%CI:321-3723)例.研究结果将可为相关部门制定手足口病防控措施提供决策依据.     

Turing pattern selection in a reactionben diffusion epidemic modelast

We present Turing pattern selection in a reaction—diffusion epidemic model under zero-flux boundary conditions. The value of this study is twofold. First, it establishes the amplitude equations for the excited modes, which determines the stability of amplitudes towards uniform and inhomogeneous perturbations. Second, it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication: on increasing the control parameter v, the sequence “H₀ hexagons → H₀-hexagon-stripe mixtures → stripes → H_π-hexagon-stripe mixtures → H_π hexagons” is observed. This may enrich the pattern dynamics in a diffusive epidemic model.     

一类含时滞与收获的捕食系统的Hopf分支分析(英文)

运用定性分析和分支理论,研究了一类含时滞与收获的Monod-Haldane型捕食系统的动力学行为,确定了Hopf分支发生时的时滞τ的临界条件,并通过规范型理论和中心流行定理,研究了Hopf分支的方向与稳定性等.最后,利用数值模拟验证了研究结果.     

Turing pattern selection in a reaction-diffusion epidemic model

We present Turing pattern selection in a reaction-diffusion epidemic model under zero-flux boundary conditions.The value of this study is twofold.First,it establishes the amplitude equations for the excited modes,which determines the stability of amplitudes towards uniform and inhomogeneous perturbations.Second,it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication:on increasing the control parameter ν,the sequence "H 0 hexagons → H 0-hexagon-stripe mixtures → stripes → H π-hexagon-stripe mixtures → H π hexagons" is observed.This may enrich the pattern dynamics in a diffusive epidemic model.