数学代写|数学生态学作业代写Mathematical Ecology代考|Principles and Tools of Mathematical Modeling

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我们提供的数学生态学Mathematical Ecology及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等楖率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等楖率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
数学代写|数学生态学作业代写Mathematical Ecology代考|Principles and Tools of Mathematical Modeling

数学代写|数学生态学作业代写Mathematical Ecology代考|Role and Stages of Mathematical Modeling

Mathematical modeling is a vital component of scientific research and policy making. Its effectiveness has been proven for centuries. The modeling provides an explanation and prediction of the behavior of complex economic and environmental systems and helps to obtain new theoretical knowledge about the nature and society. The concept of the economic-environmental system assumes the influence of both the economy and environment on each other and the possibility of human control in the system [7]. The importance of modeling of such systems increases proportionally to the scale of human impact on the environment.

Mathematical modeling and computer simulation have a special place among scientific methods. The advantages of modeling as compared to experimentation are as follows:

  • Universal availability and applicability of modeling tools.
  • Low costs and short timeline of the modeling process.
  • Multiple simulations on a wide range of model parameters (“what-if” analysis).
  • Possibility of making various model modifications and improvements.
  • Evading negative outcomes of real experiments, and others.

Modeling should begin at the early stage of a study, just after initial observation or experimentation. It can take decades to notice visible changes in environmental systems, by which time the changes may have already become irreversible. Mathematical modeling can predict negative changes in such systems and recommend measures to prevent them. The analysis of early modeling results can also suggest what kind of additional information is required and what model modifications can be made to achieve a better correspondence with the real-life picture.
A mathematical model is not a copy of the real world: it is always a simplification of the reality, which assists in revealing principal features of real phenomena. In theoretical research or decision-making practice, people use models because they do not possess an absolute knowledge of reality. The models initially emerge in the human brain. Scientific research improves and justifies such mental models, which become conceptual models in corresponding areas of science. Mathematical and computer modeling methods are based on the conceptual models and, therefore, cannot be more informative than these models. Formal mathematical models are secondary with respect to the conceptual models; however, they allow for finding new insights that are impossible to obtain by other scientific methods.

数学代写|数学生态学作业代写Mathematical Ecology代考|Mathematical Modeling and Computer Simulation

Computer modeling complements and extends traditional analytic forms of mathematical modeling. Modern computers are able to process vast amounts of data, including various choices of system evolution in a quick and efficient manner. Therefore, computer simulation has become a common additional or even primary modeling technique, especially when analytic solution is challenging or impossible to obtain. Computers are widely used in interactive modeling of complex environmental problems, such as weather prediction and global climate change.
Modeling gives a quantitative description of a real system and its connections with the external environment in the presence of unpredicted or inaccessible factors. Both traditional and computer models meet major challenges related to principal impossibility to obtain complete ecological information for modeling. At the same time, the increasing capabilities and reasonable prices of modern computers lead to the appearance of new modeling concepts entirely based on computer information processing, such as the agent-based modeling. Such models are populated by millions of computer-simulated agents that act as predicted for

living organisms. In economics, the agent-based models try to simulate elementary transactions that occur in an actual economy. This area of research is emerging, but it has not yet delivered convincing breakthroughs.

The possibilities of computer modeling and simulation should not be overestimated because computer models are also based on original conceptual models of specific disciplines. In any scenario, traditional mathematical modeling keeps its place and relevance in the predictable future, as both a learning and decision-support tool.

数学代写|数学生态学作业代写Mathematical Ecology代考|Choice of Models

Deterministic models operate with certain quantitative characteristics of systems and processes without assuming their probabilistic nature. Deterministic models are helpful in many realistic situations that involve relatively few sources of

uncertainty inside the system. In modeling practice, deterministic models can deal with the averaged probabilistic characteristics of processes under study (an average “concentration of pollutant” instead of the real concentration, the expected value of “equipment lifetime” instead of the real equipment lifetime, and so on) and are based on the approximation of a real process.

Economic and environmental systems belong to complex systems with high dimensionality and uncertainty of the relationships inherent in them. Nevertheless, the subsequent chapters demonstrate that deterministic models are commonly used for their description. In many cases, increasing complexity of mathematical description using stochastic factors does not lead to substantial insight into the nature of a problem.

Stochastic models describe connections among stochastic (probabilistic) characteristics of systems and processes under study. They are useful for the analysis of repetitive processes and usually require a large amount of data to start modeling. Implementation of economic and environmental processes is unique and accompanied by a shortage of data (especially for large-scale systems). A comprehensive analysis of all available information should be the first step of the system analysis. A majority of the models in this textbook are deterministic. Stochastic models are used in Sect. $10.2$ due to a substantially stochastic nature of the natural resource discovery.

数学代写|数学生态学作业代写Mathematical Ecology代考|Principles and Tools of Mathematical Modeling


数学代写|数学生态学作业代写Mathematical Ecology代考|Role and Stages of Mathematical Modeling



  • 建模工具的普遍可用性和适用性。
  • 建模过程成本低且时间短。
  • 对各种模型参数进行多次模拟(“假设”分析)。
  • 可以进行各种模型修改和改进。
  • 逃避真实实验和其他实验的负面结果。


数学代写|数学生态学作业代写Mathematical Ecology代考|Mathematical Modeling and Computer Simulation




数学代写|数学生态学作业代写Mathematical Ecology代考|Choice of Models




随机模型描述了所研究的系统和过程的随机(概率)特征之间的联系。它们对于分析重复过程很有用,并且通常需要大量数据才能开始建模。经济和环境过程的实施是独一无二的,并且伴随着数据短缺(特别是对于大型系统)。对所有可用信息的全面分析应该是系统分析的第一步。本书中的大多数模型都是确定性的。随机模型用于 Sect。10.2由于自然资源发现的基本随机性。

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。



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