Bifurcations, chaos, organized structures, and some ecological principles in discrete-time predator-prey models

Abstract

Study on population dynamics has long been a subject of interest. Within the realm of population ecology, significant focus is gathered by the dynamics exhibited by interactions of predator and prey species. Understanding the complex behaviors that arise in these systems is crucial for predicting and managing ecosystems. Continuous and discrete-time models are indeed two commonly used mathematical frameworks in population dynamics. While both types of models have their own applications and are used in describing appropriate ecosystem dynamics. There has been an increasing recognition that discrete-time models can provide a more appropriate and realistic representation of certain ecological systems. Discrete-time models are particularly well-suited for populations with non-overlapping generations. Examples of such populations include annual plants or insect species with one generation per year. One key feature of discrete-time models is that they can capture complex and rich dynamics even in lower-dimensional systems.