2024年美赛MCM/ICM报名正式开启！（附23年美赛O奖A篇优秀论文）

2024年美赛MCM/ICM报名正式开启！

（附23年美赛O奖A篇优秀论文）

1.3 Existing Literature Prior to developing our customized model, we researched and analyzed several existing models.Below are two important examples. First, we examined the classic Lotka-Volterra Model as a basis to consider competition between plant species and impacts on growth [ 6] . An abstracted version of the predator-prey equations are: dx = ax-Bxy dydry-oy where a and are the growth rates of each of the prey predator species respectively, while B and o represent the competitive interaction between the two species. Although the Lotka-Volterra Model provided a method to factor in competition, we believed its specificity towards a predator-prey relationship made it difficult to accurately model plant interactions since those interactions could potentially also be mutually beneficial. At the same time, perhaps the most important issue regarding the model for our task was the assumption of a constant growth rate. It does not take into consideration the relationship that growth rate and water scarcity. To address this resource utilization aspect of plant modeling we also considered Monod’s equation for modeling microbial growth rate [ 71 μ=μaxKs+S where , the growth rate, is determined by the product of the maximum growth rate and a fraction where S represents the concentration of a limiting substrate, or resource and K is a constant. These two models provided a fundamental starting point for our work but were ultimately insufficient for the problem at hand. In particular, we hoped to account for the following factors that were not considered in these systems: I. Multiple species interaction 2. Storage of groundwater 3. The spatial dimensions of the community, which infiuences plant and water dispersal 4. Different types of droughts 5. Resilience and resistance of plants 6. Exteral factors like pollution and habitat reduction .