Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response

In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.

The Model of Poverty Alleviation and Income Growth by Developing Plateau-characterized Agriculture and Its Achievements Analysis in Yunnan Province——a Case Study in Midu County, Dali Bai Autonomous Prefecture

The policy of taking the targeted poverty alleviation measures has been the mission of the age in propelling the 13th Five-year Plan and building moderately prosperous society. A good poverty alleviation model is of significance for the goal. The research introduced a poverty-stricken county-Midu County, Dali Bai Au- tonomous Prefecture, analyzed the basic approaches and the main achievements of ＂the model of poverty alleviation and income growth by developing plateau-charac- terized agriculture＂, and proposed some suggestions to promoting and applying this model. The research provides references for plateau-characterized agricultural devel- opment and targeted poverty alleviation strategy.

Turing pattern selection for a plant-wrack model with cross-diffusion

We investigate the Turing instability and pattern formation mechanism of a plant-wrack model with both self-diffusion and cross-diffusion terms.We first study the effect of self-diffusion on the stability of equilibrium.We then derive the conditions for the occurrence of the Turing patterns induced by cross-diffusion based on self-diffusion stability.Next,we analyze the pattern selection by using the amplitude equation and obtain the exact parameter ranges of different types of patterns,including stripe patterns,hexagonal patterns and mixed states.Finally,numerical simulations confirm the theoretical results.

变温条件下解析Preisach磁滞模型误差修正和特征参数辨识方法

温度升高会影响磁性材料的磁滞特性,从而改变电气设备的性能。目前解析Preisach模型无法对温度进行有效表征,导致损耗计算结果误差较大。为此,本文首先分析了基于Lorentzian函数的解析Preisach模型特征参数对磁滞回线形状参数的影响程度,如饱和磁通密度、矫顽力、剩磁等,研究了不同温度下模型参数和材料磁特性的变化。根据模型特征参数具有的磁滞回线形状相关性和温度相关性,引进温度系数来修正模型特征参数,构建变温条件下的解析Preisach模型,并给出了计及温度影响的模型参数辨识方法。最终实验测量纳米晶合金在变温条件下的极限磁滞回线,对多组实测值和修正后的解析Preisach模型计算值进行对比后,得出在饱和磁通密度、矫顽力和剩磁处修正模型结果的平均相对误差分别为0.15%、2.21%、5.76%,证明了该修正模型的准确性。

管道环焊缝拉伸应变容量模型分析及改进

为了确保石油天然气管线在复杂服役环境下的本质安全,探讨了目前国内外广泛应用的3种管道环焊缝拉伸应变容量模型(CSA Z662、PRCI-CRES、EXXON MOBIL),并对其参数选取范围性进行了汇总和对比分析。通过分析模型预测值和96组全尺寸管道及宽板拉伸试验数据的差异,对各拉伸应变容量模型在不同钢级下的预测精度进行了验证,并使用90%置信上限倒数法计算了模型安全系数。结果表明:由于CSA Z662模型断裂韧性取值上限过小,导致其对于中、高钢级管线的预测值过于保守;EXXON MOBIL和PRCI-CRES模型更为完善,二者预测结果相似,并与试验结果较为相符。针对EXXON MOBIL和PRCI-CRES模型计算所得的安全系数可以明显改善模型预测结果,可将非保守预测值最大误差控制在约30%范围内,从而有效满足较为保守的设计要求。研究结果可为管线基于应变设计提供理论指导。

基于BP神经网络的集中供热二次网回水温度预测控制研究

针对集中供热系统二次管网存在的水力失调问题,设计了二次网水力平衡调节及回水温度预测模型,并实施智能控制策略,以实现二次网回水温度的精准控制。首先,构建BP神经网络预测模型,将此模型的输出视为二次网回水温度给定值;其次,在整个系统控制中,实施BP神经网络与PID控制器相结合的策略,进行二次网回水温度的控制。以高邑县某小区换热站数据为基础,通过阶跃响应曲线法建立二次网回水温度控制系统的数学模型,并通过BP-PID控制进行仿真实验。实验结果表明,与传统PID控制器相比,BP-PID控制器具有调节时间短、超调量小的优点,能够快速达到平稳状态。

如何测试ChatGPT的语义理解与常识推理水平?——兼谈大语言模型时代语言学的挑战与机会

ChatGPT等大语言模型在语义理解和常识推理方面表现优秀,其技术奥秘在于模型开发者在对词语进行向量表示时,遵循分布式语义学原理,采用了“嵌入”这种代数方法。但是,经典的测试语言运用等智能水平的“图灵测试”,难以识别欺骗和回避等作弊手段,因此,计算机科学家设计了“新图灵测试”,其中的威诺格拉德模式挑战与语言学关系密切。这一模式以代词消歧为测试点设计句子对和问题,但是经过大规模语料训练的语言模型可以凭借词汇上的统计相关性,而不是靠真正理解句子的意义来给出正确答案。为克服这一缺陷,学者们又发展出WinoGrande数据集,提高了数据的规模和难度,确保它们无法通过网络搜索等手段来得到正确答案。我们用威诺格拉德模式设计了无偏向双重句子对测试ChatGPT,展示了大语言模型在语义理解和常识推理方面已达到接近人类的水平。当然,从具身模拟假说来看,大语言模型不可能像人一样富有体验性地理解人类自然语言。最后,我们呼吁:语言学家应该积极参与构建WinoGrade测试集之类的工作,在人工智能时代扩展自身的学术研究领域。

带有时滞和收获的扩散捕食系统的斑图动力学分析

文章研究了一类带有食饵收获效应和时滞的捕食系统的Turing斑图的形成及选择问题。首先利用稳定性理论给出了由交叉扩散项引起的Turing不稳定条件和分支理论分析,得到了系统Turing斑图的存在区域。然后利用Matlab软件对系统Turing斑图的形成和选择结果进行了数值模拟。这为以后带有交叉扩散的时滞反应扩散系统的研究提供了可行的方法,具有广泛的理论应用价值。

扩散和时滞影响下病毒感染模型的Turing不稳定性和Hopf分岔

考虑反应扩散和时滞因素,研究了病毒感染模型的Turing不稳定性和Hopf分岔.首先,给出无时滞情形下的Turing不稳定条件;其次,选择时滞为分岔参数,得到Hopf分岔的判据,同时给出分岔阈值的解析表达;最后,通过数值模拟仿真验证了理论结果的正确性.

基于结构化特征重构的高光谱图像分类

特征提取是高光谱图像分类的关键.现有分类方法在特征提取时,往往忽略特征的信息保有量和空间分布等因素,导致输出的特征可能面临低信息保有量与无序分布等问题,预测结果不佳.为此,本文提出一种基于结构化特征重构的高光谱图像分类方法,能够有效地减少特征提取过程中信息丢失,提高信息保有量,并充分考虑特征的空间分布,增强特征的判别性.借鉴重构思想以及自表达理论,建立结构特征重构的特征表示模型,可提升图像信息的利用率,并描述反映有序分布的结构信息.针对建立的多变量模型,设计一种基于交替更新的优化策略来求解模型.利用支持向量机来对特征进行分类计算和标签预测.利用Salinas、Pavia Center、Botswana以及Houston数据进行实验验证,结果表明,本文算法优于现有的分类模型,在OA(Overall Accuracy)、AA(Average Accuracy)以及Kappa系数等指标上平均提升了2.6%、3.9%、3.3%.

致密储层缝内暂堵转向压裂裂缝扩展规律数值模拟

基于损伤力学理论,建立了储层渗流-应力-损伤耦合裂缝扩展数值模型,将模型结果与室内真三轴水力压裂物理模拟实验结果进行了对比,验证了模型的准确性,并基于该模型探讨了压裂液黏度、排量、水平地应力差以及储层岩石非均质性对缝内暂堵转向压裂效果的影响。研究结果表明:(1)储层渗流-应力-损伤耦合裂缝扩展数值模型是联合流体流动控制方程与岩石变形方程形成整体控制方程,通过在初始裂缝扩展路径上某一区域人为设置高强度的岩石物理力学参数和较小的储层渗透率值,实现缝内暂堵的模拟。(2)缝内暂堵转向压裂裂缝扩展模型数值模拟的分支缝数量、主裂缝面积、主裂缝延伸方向等与室内真三轴水力压裂物理模拟实验的结果基本一致,该模型可实现缝内暂堵后基质的破裂与新裂缝扩展模拟,对缝内暂堵转向压裂裂缝扩展情况也具有较好的模拟效果。(3)压裂液的黏度和排量越大,缝内暂堵转向压裂裂缝长度、改造面积及偏转角度均明显增大,且逐渐由单一裂缝向复杂裂缝转变。当水平地应力差小于7.5 MPa时,缝内暂堵转向压裂的效果较好;当水平地应力差为10~15 MPa时,压裂效果变差;当水平地应力差大于15 MPa时,裂缝几乎不偏转;储层非均质性会影响裂缝局部的扩展路径,但对裂缝总体扩展趋势影响甚微。

一类比率依赖的捕食者-食饵扩散系统的动力学性质分析

研究了一类具比率依赖型功能反应的捕食者-食饵系统的时空动力学行为。为了探讨食饵的内禀增长率和扩散系数比值对系统动力学性质的影响,进行了以下分析:平衡解的稳定性分析;Hopf分支、Turing分支和Turing-Hopf分支出现的充分条件;Turing-Hopf分支点附近规范型的推导和计算。结果表明,食饵内禀增长率和扩散系数比值的微小变化会破坏系统常值稳态解的稳定性,引起复杂的时空行为,包括空间齐次周期解、空间非齐次周期解和非常值稳态解。此外,结合数值模拟对理论分析的结果进行了解释,数值模拟的结果和理论分析完全吻合。

Spatial Pattern Induced by Cross-Diffusion in a Chemostat Model with Maintenance Energy

A chemostat model with maintenance energy and crossdiffusion is considered,and the formation of patterns is caused by the cross-diffusion. First, through linear stability analysis, the necessary conditions for the formation of the spatial patterns are given. Then numerical simulations by changing the values of crossdiffusions in the unstable domain are performed. The results showthat the cross-diffusion coefficient plays an important role in the formation of the pattern, and the different values of the crossdiffusion coefficients may lead to different types of pattern formation.

An Empirical Study of Good-Turing Smoothing for Language Models on Different Size Corpora of Chinese

Data sparseness has been an inherited issue of statistical language models and smoothing method is usually used to resolve the zero count problems. In this paper, we studied empirically and analyzed the well-known smoothing methods of Good-Turing and advanced Good-Turing for language models on large sizes Chinese corpus. In the paper, ten models are generated sequentially on various size of corpus, from 30 M to 300 M Chinese words of CGW corpus. In our experiments, the smoothing methods;Good-Turing and Advanced Good-Turing smoothing are evaluated on inside testing and outside testing. Based on experiments results, we analyzed further the trends of perplexity of smoothing methods, which are useful for employing the effective smoothing methods to alleviate the issue of data sparseness on various sizes of language models. Finally, some helpful observations are described in detail.

Turing pattern in the fractional Gierer–Meinhardt model

It is well-known that reaction–diffusion systems are used to describe the pattern formation models. In this paper,we will investigate the pattern formation generated by the fractional reaction–diffusion systems. We first explore the mathematical mechanism of the pattern by applying the linear stability analysis for the fractional Gierer–Meinhardt system.Then, an efficient high-precision numerical scheme is used in the numerical simulation. The proposed method is based on an exponential time differencing Runge–Kutta method in temporal direction and a Fourier spectral method in spatial direction. This method has the advantages of high precision, better stability, and less storage. Numerical simulations show that the system control parameters and fractional order exponent have decisive influence on the generation of patterns. Our numerical results verify our theoretical results.

具有区间参数的传染病模型斑图动力学研究

建立了一个具有区间参数的传染病模型,利用区间值函数和线性稳定性分析给出了该模型产生图灵斑图的条件,数值模拟得到了当有效接触率和扩散系数分别为区间参数时染病者的图灵斑图。结果表明,随着有效接触率区间变量增加,染病者斑图结构发生显著变化:由冷点斑图变为热点-条混合斑图,染病者空间平均密度降低。该结果揭示了区间参数对染病者斑图动力学行为的影响,为传染病控制提供了新的理论依据。

Quantitative Study of Clothing Expenditure of Families with Different Education Level in shanghai

300 families were investigated,which belong to theFamily Investigation Net of Government Policy-makingInvestigating System of Shanghai Statistical Bureau.Thedata were analysed with SPSSWIN6.0 software.The re-gression models showed that families with different edu-cation level have different clothing expenditure models,that is,different affecting factors of clothing consumingin the second quarter.High education families’clothingexpenditure is mainly affected by the family living spaceand husband’s income,while middle education familiesby wife’s occupation and low education farmilies by hus-band’s income.The descriptive statistics showed:fromApril to June,families with different education levelwere quite different on the following aspects:(1)theclothing expenditure of the whole family and its mem-bers;(2)the structure of clothing consuming;(3)thepurchasing price of clothing;(4)the selection of clothingpurchase places.

带收获率的Lotka-Volterra捕食者-食饵趋化扩散模型的Turing不稳定性

为了解一类带收获率的Lotka-Volterra捕食者-食饵趋化扩散模型的Turing不稳定性,应用线性化方法证明了趋化扩散具有不稳定性作用,能产生Turing斑图,并运用数值解验证了所得结论.

具有可逆效应的自催化扩散模型的定性分析

在齐次Neumann边界条件下,研究一类具有可逆效应的自催化扩散模型.首先,通过稳定性理论建立由扩散引起的Turing不稳定性;其次,利用Crandall-Rabinowitz局部分支理论,给出简单特征值处的分支结构;最后,采用空间分解技术和隐函数定理,证明双特征值处稳态分支的存在性.

反应扩散Schnakenberg系统周期解的图灵不稳定性

针对生化反应中的周期振荡现象,讨论一类具有齐次Neumann边界条件的Schnakenberg模型.利用Hopf分支理论、中心流形理论、规范型方法以及扰动理论等方法,给出反应扩散Schnakenberg系统的Hopf分支周期解的存在性、稳定性以及图灵不稳定性.