Singularity: A maple Library for Local Zero Bifurcation Control of Scalar Smooth Maps

Abstract

Singularity theory is designed for the local bifurcation analysis and control of singular phenomena. The theory has a significant technical computational burden. However, there does not exist any (symbolic) computer library for this purpose. We suitably generalize some powerful tools from algebraic geometry for correct implementation of the results in singularity theory. We provide some required criteria along with rigorous proofs for efficient and cognitive computer implementation. Our results also address permissible truncation degrees in Taylor expansions of smooth bifurcation maps. Accordingly, an end-user friendly maple library, named “singularity,” is developed for an efficient bifurcation analysis and control of real zeros of scalar smooth maps. We have further written a comprehensive user guide for singularity. The main features of our developed maple library are briefly illustrated along with a few examples.