A Graphical-Based Method for Plotting Local Bifurcation Diagram

TL;DR

This paper introduces a simple, graphical algorithm for plotting local bifurcation diagrams, making it easier for students to understand dynamical systems without complex calculations.

Contribution

It presents a novel, educational algorithm for manually and quickly plotting local bifurcation diagrams, enhancing learning in dynamical systems courses.

Findings

Algorithm is effective for educational examples

Students find the method simpler than traditional mathematical plotting

Validated on multiple dynamical system examples

Abstract

Bifurcation diagram is a powerful tool that visually gives information about the behavior of the equilibrium points of a dynamical system respect to the varying parameter. This paper proposes an educational algorithm by which the local bifurcation diagram could be plotted manually and fast in an easy and straightforward way. To the students, this algorithmic method seems to be simpler and more straightforward than mathematical plotting methods in educational and ordinary problems during the learning and studying of courses related to dynamical systems and bifurcation diagrams. For validation, the algorithm has been applied to several educational examples in the course of dynamical systems.