2023年美國HIMCM中學數學建模競賽A題

文章目錄[隱藏]

中文賽題：蒲公英，是敵是友？
- 術語表
- 參考資料
Problem: Dandelions: Friend? Foe? Both? Neither?
- Glossary
- References

中文賽題：蒲公英，是敵是友？

蒲公英（學名Taraxacum officinale）是一種原產(chan) 於(yu) 歐亞(ya) 大陸的植物，現在可以在全球範圍內(nei) 找到^[1]。這種植物以其鮮豔的黃色花朵（圖1）和獨特的“絨球”種子頭（圖2）而容易識別。

圖 1圖 2種子頭上的每顆種子都連接到一個(ge) 類似降落傘(san) 的結構，被稱為(wei) “冠毛”，這種結構有助於(yu) 蒲公英通過風來傳(chuan) 播種子^[2]。

如果一個(ge) 處於(yu) “絨球”階段的蒲公英鄰近一個(ge) 開放的一公頃土地，請你創建一個(ge) 數學模型，以預測蒲公英在1、2、3、6和12個(ge) 月內(nei) 的傳(chuan) 播情況。你的模型需要考慮各種氣候條件（如溫帶、幹旱和熱帶氣候）對蒲公英生長的影響。
蒲公英、人類和其他植物之間的關(guan) 係是複雜的。由於(yu) 這種植物能夠在不同環境中茁壯成長，因此有些人認為(wei) 蒲公英是令人討厭的雜草或入侵物種。但是蒲公英的每個(ge) 部分都可以食用，而且蒲公英在藥用和烹飪方麵有豐(feng) 富的曆史。請建立一個(ge) 能夠確定入侵物種“影響因子”的數學模型。該模型應該整合多個(ge) 變量，包括植物的特征以及它對環境造成的傷(shang) 害性質和程度。
- 使用你的模型計算蒲公英的影響因子來測試該模型。
- 你需要選擇另外兩種通常被認為是入侵物種的植物，然後應用你的模型來計算它們的影響因子。確保標識出每種植物在哪個地區被視為入侵物種。

您的 PDF 解決(jue) 方案總頁數不得超過25頁，包括：

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目錄。
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術語表

“入侵物種”是指：

對於(yu) 考慮的生態係統來說，是非本地（或外來的）的物種；
並且，其引入會(hui) 或可能會(hui) 危害經濟、環境或人類健康。

非本地物種是指在其自然分布地區之外生存的植物或動物。不要將“非本地物種”和“入侵物種”混淆。許多常見的水果和蔬菜並非原產(chan) 於(yu) 美國。例如，番茄和辣椒起源於(yu) 南美洲，而生菜最早在埃及種植。家養(yang) 的牛對北美洲來說並非本地物種，它們(men) 作為(wei) 食物被引入，被視為(wei) 農(nong) 業(ye) 環境中的有益生物。

來源：美國農(nong) 業(ye) 部國家入侵物種信息中心^[3]。

參考資料

[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].