Modeling Competitive Interactions Between Two Species Using Logistic Growth
This article formulates a logistic‑based mathematical model for two interacting species, outlines assumptions about their independent growth and mutual inhibition, and examines how competitive strength determines outcomes such as extinction of the weaker species and the stronger reaching its carrying capacity.
Problem
Two populations coexist in a natural environment with relationships: competition, mutual dependence, or predator‑prey.
When they compete for the same food and space, the typical outcome is extinction of the weaker competitor and the stronger reaching the environment’s carrying capacity.
Establish a mathematical model describing the competitive process and analyze the conditions leading to this outcome.
Model Assumptions
Populations A and B each follow logistic growth when isolated.
When coexisting, the inhibitory effect of B on A’s growth is proportional to B’s size, and vice versa.
Model
For the resources consumed by population A, population B exerts a larger inhibitory effect, indicating that B has stronger competitive ability.
Various Forms of Two‑Population Models
Competition
Mutual dependence
Predator‑prey (the strong eat the weak)
Model Perspective
Insights, knowledge, and enjoyment from a mathematical modeling researcher and educator. Hosted by Haihua Wang, a modeling instructor and author of "Clever Use of Chat for Mathematical Modeling", "Modeling: The Mathematics of Thinking", "Mathematical Modeling Practice: A Hands‑On Guide to Competitions", and co‑author of "Mathematical Modeling: Teaching Design and Cases".
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