Logistic Map Program for Chaotic Population Model

This section introduces the classic mathematical model in chaos theory - the population dynamics model, commonly known as the insect population model. The population model serves as a mathematical tool for describing changes in insect population numbers. It is based on the logistic mapping algorithm, which aims to simulate the dynamic changes in insect populations through iterative calculations. The core algorithm can be implemented using a simple recursive function: x_n+1 = r * x_n (1 - x_n), where 'r' represents the growth rate parameter and 'x' denotes the population ratio. This model finds widespread applications in ecology and environmental science, helping researchers better understand ecosystem change patterns. Key programming considerations include parameter tuning for different chaotic regimes and bifurcation analysis. The research significance of the population model cannot be underestimated, as it provides crucial reference value for predicting and maintaining ecosystem stability through computational simulations.