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An Integro-difference Model of Dandelions Spreading

Author(s)

Yuanbo Cui1,*, Dufenpei Zhao2, Ziqian Dai3, Jiarui Wang3

Affiliation(s)

1Wlsa Shanghai School (Zhengxi Campus), No. 88 Guotai Road Yangpu District, Shanghai, China 2Beijing 21st Century School, No. 46 Enjizhuang Haidian District, Beijing, China 3Beijing Yizhuang Experimental Middle School, No. 12 Sihao Road Daxing District, Beijing, China *Corresponding Author.

Abstract

Dandelions have a significant impact on the ecological environment and possess certain economic value. The purpose of this paper is to present an effective mathematical model for predicting the distribution of dandelions. The model is based on the concept of integro-difference equations (IDE), which are particularly effective for modeling the propagation of species with strongly synchronized life stages, influenced heavily by seasonal changes. To utilize the IDE for predicting the spread of dandelions, it is essential to understand the population growth rate of the species. The concept of the logistic model is employed to estimate the population of dandelions. By integrating these mathematical tools, the paper were able to study the spread and growth of dandelions across different seasons and varying conditions, yielding data that forms a normal distribution by distance. As an application, the distribution of dandelions in three different ecological environments is predicted. Additionally, a mathematical model was developed to determine an ‘impact factor’ for invasive species. This model integrates multiple variables, including the characteristics of the plant and the nature and extent of the harm it inflicts on its environment. The simulation results demonstrate that the model exhibits good predictive performance.

Keywords

Dandelion Distribution; Integro-Difference Equation; Gaussian Distribution; Multivariate Analysis

References

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