2023年美国HIMCM中学数学建模竞赛A题

文章目录[隐藏]

中文赛题：蒲公英，是敌是友？
- 术语表
- 参考资料
Problem: Dandelions: Friend? Foe? Both? Neither?
- Glossary
- References

中文赛题：蒲公英，是敌是友？

蒲公英（学名Taraxacum officinale）是一种原产于欧亚大陆的植物，现在可以在全球范围内找到^[1]。这种植物以其鲜艳的黄色花朵（图1）和独特的“绒球”种子头（图2）而容易识别。

图 1图 2种子头上的每颗种子都连接到一个类似降落伞的结构，被称为“冠毛”，这种结构有助于蒲公英通过风来传播种子^[2]。

如果一个处于“绒球”阶段的蒲公英邻近一个开放的一公顷土地，请你创建一个数学模型，以预测蒲公英在1、2、3、6和12个月内的传播情况。你的模型需要考虑各种气候条件（如温带、干旱和热带气候）对蒲公英生长的影响。
蒲公英、人类和其他植物之间的关系是复杂的。由于这种植物能够在不同环境中茁壮成长，因此有些人认为蒲公英是令人讨厌的杂草或入侵物种。但是蒲公英的每个部分都可以食用，而且蒲公英在药用和烹饪方面有丰富的历史。请建立一个能够确定入侵物种“影响因子”的数学模型。该模型应该整合多个变量，包括植物的特征以及它对环境造成的伤害性质和程度。
- 使用你的模型计算蒲公英的影响因子来测试该模型。
- 你需要选择另外两种通常被认为是入侵物种的植物，然后应用你的模型来计算它们的影响因子。确保标识出每种植物在哪个地区被视为入侵物种。

您的 PDF 解决方案总页数不得超过25页，包括：

一页摘要页。
目录。
完整解决方案。
参考文献列表。
AI使用报告（如果使用不计入 25 页总限制）。

注意：HiMCM 提交的完整解决方案没有特定的最低页数要求。您可以使用最多 25 页的总页数来展示您所有的解决方案工作和任何您想包含的额外信息（例如：图纸、图表、计算、表格）。部分解决方案也是可以接受的。我们允许谨慎使用AI，如ChatGPT。如果你选择使用生成性 AI，就必须遵守 COMAP AI 使用政策：你必须在 PDF 解决方案文件的末尾添加一个额外的 AI 使用报告，这个报告不计入您解决方案的 25 页总页数限制。

术语表

“入侵物种”是指：

对于考虑的生态系统来说，是非本地（或外来的）的物种；
并且，其引入会或可能会危害经济、环境或人类健康。

非本地物种是指在其自然分布地区之外生存的植物或动物。不要将“非本地物种”和“入侵物种”混淆。许多常见的水果和蔬菜并非原产于美国。例如，番茄和辣椒起源于南美洲，而生菜最早在埃及种植。家养的牛对北美洲来说并非本地物种，它们作为食物被引入，被视为农业环境中的有益生物。

来源：美国农业部国家入侵物种信息中心^[3]。

参考资料

[1]Getting to Know Common Dandelion:https://anpc.ab.ca/wp-content/uploads/2015/01/dandelion.pdf

[2]Dandelion, Taraxacum officinale:https://hort.extension.wisc.edu/articles/dandelion-taraxacum-officinale

[3]What are Invasive Species?:https://www.invasivespeciesinfo.gov/what-are-invasive-species

Problem: Dandelions: Friend? Foe? Both? Neither?

Taraxacum officinale, commonly referred to as the dandelion, is a plant native to Eurasia that can now be found worldwide^[1]. This plant is easily identifiable by its bright yellow flowers (Figure 1) and its distinctive “puffball” seed head (Figure 2).

Figure 1Figure 2

Each seed from this head is attached to a parachute-like structure, known as a 'pappus', which facilitates wind dispersal^[2].

If a single dandelion in its “puffball” stage is adjacent to an open one-hectare plot of land, create a mathematical model to predict the spread of dandelions over the course of 1, 2, 3, 6, and 12 months. Make sure your model incorporates the effects of various climatic conditions, such as temperate, arid, and tropical climates, on dandelion growth.
The relationship between dandelions, humans, and other flora is complicated. Because of the plant’s ability to thrive in diverse environments, some label it a pesky weed or as an invasive species. Conversely, every part of the dandelion is edible, and the plant has a rich history of medicinal and culinary use. Formulate a mathematical model capable of determining an ‘impact factor’ for invasive species. This model should integrate multiple variables, including the plant's characteristics and the nature and extent of the harm it inflicts on its environment.
- Test your model by using it to compute an impact factor for dandelions.
- Apply your model to determine the impact factor for two other plant species of your choice that are often considered invasive. Make sure to identify the region for whom each of the plants you choose are invasive.

Your PDF solution of no more than 25 total pages should include:

One-page Summary Sheet.
Table of Contents.
Your complete solution.
References list.
AI Use Report (If used does not count toward the 25-page limit.)

Note: There is no specific required minimum page length for a complete HiMCM submission. You may use up to 25 total pages for all your solution work and any additional information you want to include (for example: drawings, diagrams, calculations, tables). Partial solutions are accepted. We permit the careful use of AI such as ChatGPT, although it is not necessary to create a solution to this problem. If you choose to utilize a generative AI, you must follow the COMAP AI use policy. This will result in an additional AI use report that you must add to the end of your PDF solution file and does not count toward the 25 total page limit for your solution.

Glossary

An “invasive species” is a species that is:

non-native (or alien) to the ecosystem under consideration and,
whose introduction causes or is likely to cause economic or environmental harm or harm to human health.

Non-native species are plants and animals living in areas where they do not naturally exist. “Non-native species” and “invasive species” cannot be used interchangeably. Many commonly grown fruits and vegetables are not native to the U.S. For example, tomatoes and hot peppers originated from South America, while lettuce was first grown in Egypt. Domestic cows are nonnative to North America and were introduced as a food source, and considered to be a beneficial organism in an agricultural setting.

From USDA National Invasive Species Information Center^[3].