The Research History of Population Models

Abstract

This paper mainly introduces the research history of biological population models, especially predator-prey models. With the proposal of the most traditional and representative Lotka-Volterra model, the dynamic behavior of biological population models has become increasingly clear. The three-dimensional Lotka-Volterra model has also played a pivotal role throughout the entire research process. Clearly, scholars' thirst for knowledge drives them to be unsatisfied with studying the traditional Lotka-Volterra model. They apply previous research methods to new biological population models, and have also achieved a considerable number of research results. However, with the continuous development of computer technology, numerical simulation has become an important tool for studying biological population models, which means that the impact of adding stochastic terms such as Brownian motion, time delays, and Levy jumps to the model can be intuitively presented. This paper summarizes the different stages of research on biological population models and briefly introduces the important theoretical achievements of different representative models.