To Tackle Bifurcation Problems with Python

Abstract

Python is gaining attention as a fundamental programming language for machine learning and data science. In this paper, we describe a detailed Python approach to nonlinear problems, especially the bifurcation problems of periodic solutions. It is a highly readable implementation of the bifurcation algorithm, independent of the computer and the operating system, and it allows interactive trial-and-error processing. We describe the advantages of Python for bifurcation problems with some illustrated codes. We also show a compact implementation of computation for Neimark-Sacker bifurcation using the bialternate product and an automated process for generating the Hessian using Sympy.