Solving bifurcation diagrams using fixed points as control parameters

TL;DR

This paper introduces a novel method for solving bifurcation diagrams by using fixed point coordinates as control parameters, enabling exact solutions to complex bifurcation problems.

Contribution

It presents a new approach that transforms bifurcation analysis into a problem of fixed point coordinate control, providing a potentially exact solution method.

Findings

Enables exact solutions to complex bifurcation problems

Transforms bifurcation analysis into fixed point coordinate control

Offers a new analytical tool for bifurcation diagrams

Abstract

We propose to determine the bifurcation diagrams of fixed points using their coordinates as control parameters. This method can lead to exact solutions to otherwise intractable bifurcation problems.