Fractal Basins and Boundaries in 2D Maps inspired in Discrete Population Models

TL;DR

This paper explores complex behaviors such as multistability and fractal basin boundaries in 2D discrete population models, illustrating these phenomena through three different systems.

Contribution

It demonstrates the emergence of fractal basins and boundaries in simple 2D population models, providing visualizations and explanations of these complex dynamics.

Findings

Identification of fractal basin boundaries in models

Visualization of multistability phenomena

Analysis of complex dynamical behaviors in population models

Abstract

Two-dimensional maps can model interactions between populations. Despite their simplicity, these dynamical systems can show some complex situations, as multistability or fractal boundaries between basins that lead to remarkable pictures. Some of them are shown and explained here for three different 2D discrete models.