The Pitchfork Bifurcation

TL;DR

This paper introduces a novel theory of the Pitchfork bifurcation that eliminates the need for symmetry and the third derivative, broadening the understanding of bifurcation phenomena.

Contribution

It presents a new theoretical framework for Pitchfork bifurcation that does not rely on symmetry or third derivative conditions.

Findings

New bifurcation theory developed

Removes symmetry requirement

Eliminates need for third derivative

Abstract

We give development of a new theory of the Pitchfork bifurcation, which removes the perspective of the third derivative and a requirement of symmetry.