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Applied Mathematics Commons

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Bifurcation

Claremont Colleges

Ordinary Differential Equations and Applied Dynamics

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Full-Text Articles in Applied Mathematics

Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan Jan 2022

Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan

CMC Senior Theses

When it comes to women in professional hierarchies, it is important to recognize the lack of representation at the higher levels. By modeling these situations we hope to draw attention to the issues currently plaguing professional atmospheres. In a paper by Clifton et. al. (2019), they model the fraction of women at any level in a professional hierarchy using the parameters of hiring gender bias and internal homophily on behalf of the applicant. This thesis will focus on a key theory in Clifton et. al.’s analysis and explain its role in the model, specifically bifrucation analysis. In order to analyze …


A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio Jan 1993

A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio

All HMC Faculty Publications and Research

In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order …