Seeds are the fundamental source of dandelion life on earth, and their germination process is the first step towards plant growth. The seed germination process involves activating a complex series of biochemical reactions that transform the dandelion seed into an active and viable organism. The germination process is crucial for producing plants and flowers, and dandelions require specific environmental conditions for successful growth. In this article, we will explore the growing process of dandelion seeds, the spread of dandelions during their growth, and the impact factors for invasive species, including dandelions. In Problem 1, we answer the question from two perspectives. We first predict the population size of dandelions. We predicted the population of dandelions over the course of one, two, three, six, and twelve months in certain various climatic conditions. We first outlined the life cycle of dandelions in five stages: seed, germination, plant, flower, and seed dispersal. We defined three variables related to the dandelion life cycle as Seed (S), Germination (G), and Flowering (F); with two more additional variables, Resources (R) and Temperature (T) in a given environment, we constructed Dandelion Demography Model using the Ordinary Differential Equations (ODEs). The results showed that the number of dandelion populations gradually increased in summer, and with the advent of autumn and winter, the temperature decreased, and the number of dandelions gradually decreased to 0. After that, we set the average temperature for the whole year higher and carried out the sensitivity analysis of the model. The results showed that dandelion populations could increase more in one year and even in autumn and winter as the temperature increased. We then used Gaussian equations in conjunction with the wind to predict the extent of dandelion coverage. The results show that in the absence of wind, the population will spread outward uniformly. Under windy conditions, the population will concentrate more in the direction of the wind, but the population density decreases as the distance from the mother plant increases. In Problem 2, we continued to study three plant species, including dandelions. We applied the hybrid entropy weight method EWM-TOPSIS model to develop an index-based measurement to determine impact factors for three invasive species: Taraxacum officinale, Amaranthus palmeri, and Alternanthera philoxeroides. EWM is used to calculate the weight of each index and reduce the disadvantages of TOPSIS, which adopts equal weights. The results showed that the influence factors of the three plants were 0.51, 0.69, and 0.71, respectively. After that, we verified the reasonableness of the model by querying the distribution of the plants worldwide.
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