# HI THERE! Iâ€™M JOSEPH JOHNSON

I am currently a PhD Candidate in Engineering Sciences and Applied Mathematics at Northwestern University. I am interested in studying nonlinear phenomena that arise in social and physical systems.

## My Research

I use dynamical systems in order to model social and biological phenomena!

### BIMODALITY IN ADVERTISING

In this project, we investigated competition of firms in market via advertising. We showed that under a small number of assumptions that firms will naturally split off into a name-brand group, which advertises at a high rate and generic brand group, which advertises virtually nothing.

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In-progress: J.D. Johnson, A. Redlich, D.M. Abrams ``A Minimal Mathematical Model for Free Market Competition Through Advertising''

### EMERGENCE OF TWO SEXES

Here we developed a mathematical model to provide an argument as to how anisogamy, having sex cells of different sizes between the mating types, arose from an isogamous population, a population having the same size of sex cells.

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In-progress: N. White, A. Kangabire, D.M. Abrams, J.D. Johnson ``A Simple Model of the Development of Anisogamy''

### MULTIMODALITY IN COUPLED OSCILLATORS

To describe synchrony of oscillators (e.g. neurons, flashing of fireflies, etc.), typically a mathematical model with attractive coupling is used. This usually leads to all the oscillators in agreement, but here we showed that we can get multiple groups of oscillators in agreement if we used repulsive coupling.

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Publications: J.D. Johnson, D.M. Abrams ``A Coupled Oscillator Model for the Origin of Bimodality and Multimodality''. Chaos 29, 073120 (2019)

## EDUCATION

### APPLIED MATHEMATICS, PHD

NORTHWESTERN UNIVERSITY

Advisor: Daniel M. Abrams

Research: Multimodality in Social and Biological Systems

September 2015 - September 2020 (expected)

### APPLIED MATHEMATICS, MS

UNIVERSITY OF AKRON

Master's Thesis: Modeling Monitoring of An Industry In A Game-Theoretic Framework with Imperfect Information

Link:

August 2013 - May 2015

### APPLIED MATHEMATICS, BS

UNIVERSITY OF AKRON

Double Major in Economics, Graduated Summa Cum Laude

August 2010 - May 2015

###### Teaching

###### Northwestern University

# MULTIVARIABLE CALCULUS

Northwesternâ€™s EXCEL program, a 5-week summer program for

a diverse set of incoming freshmen. I developed and applied active learning techniques for this

course. (2017 - 2019)

# Engineering Analysis 4 ( Head TA)

a course that covers analytical and numerical methods to solve ordinary

differential equations. This course typically has over 150 students. (2017 - 2018)

Here's a short video about understanding eigenvalues and eigenvectors geometrically!

# Mulitvariable Integration and Vector Calculus (TA)

this class focuses on multiple integration in cartesian, cylindrical, and spherical coordinates, culminating with line and surface integrals.

(2016)

###### The University of Akron

# PRECALCULUS

an introductory course to develop concepts needed for Calculus. (2014 - 2015)

# INTERMEDIATE ALGEBRA

an introductory algebra course to bring students up to speed for math-

ematics at the college level. (2013 - 2014)

###### News

###### Web Articles

# Student Feature - Joseph Johnson

I wrote piece about my time at Northwestern University! https://dsweb.siam.org/The-Magazine/Article/student-feature-joseph-johnson. (2017 - 2019)

# Dynamics Days US 2020 Recap

I wrote a recap for Dynamics Days US 2020. It was an exciting event with many engaging talks. https://dsweb.siam.org/The-Magazine/All-Issues/dynamics-days-us-2020-recap