Student Research Projects

Supervised by Bruce B. Peckham

Graduate Students

  1. BJ Olsen
    Master's thesis: "Bifurcations of Piecewise Continuous Functions"
    Graduated: 1994.
  2. Jason Puckett
    Master's project: "Computing Periodic Orbits"
    Graduated: 1995.
  3. Zbigniew Wdowiak
    Master's project: "Newton's and Burgstahler's Root Finding Methods"
    Graduated: April, 1996.
  4. Colleen Frost
    Master's project: "A comparison study of the SIS and SIRS Epidemic Models"
    Graduated: August, 1996.
  5. Jon Drexler
    Master's project: "A nonanalytic perturbation of the complex quadratic map"
    Graduated: August, 1996.
  6. Diana Colt
    Master's project: "Seasonal Disruption in Elementary Models of Insect Epidemics"
    Graduated: August, 1999. (Primary advisor was Harlan Stech.)
  7. Angela Cates
    Master's project: "A Mathematical Investigation of the Decomposition of Leaf Litter"
    Graduated: March, 2000. (Primary advisor was Harlan Stech.)
  8. Cosmin Deciu
    Master's project: "Some Aspects of Homoclinic Orbits in a Henon-like Map"
    Graduated: September, 2000.
  9. Steve Law
    Master's project: "Lyapunov Exponents"
    Graduated: 2003.
  10. Wendy Graves
    Master's project: "A comparison of Some Simple Models of Mutualism"
    Graduated: September 2003. (Coadvised with John Pastor.)
  11. Karl Kruppstadt
    Master's project: "Newton's Method for Cubics"
    Graduated: 2004. Download project pdf here .
  12. Laura Zimmermann
    Master's project: "A Producer-Consumer Model with Stoichiometry"
    Graduated: July 2006. (Coadvised with John Pastor.)
    Download project pdf here . (30 pages)
  13. Laurence Lin
    Master's thesis: "A stoichiometric model of two producers and one consumer"
    Graduated: June 2008. (Coadvised with Harlan Stech, John Pastor.)
    Download thesis pdf file here .(90 pages)
  14. James Polsinelli
    Master's project: "Probability theory, ergodicity, and applications to dynamical systems"
    (Coadvised with Barry James.) Graduated: 2010. Download project pdf here .
  15. Garrett Taft
    Master's Thesis: "Chaos, Attractors, and the Lorenz Conjecture: Noninvertible transitive maps of invariant sets are sensitive"
    Graduated: August 2010. Download thesis pdf here .
  16. Xinyuan "Vinnie" Zhang
    Master's Project: "Enrichment in a Producer-Consumer Model with varying rates of Stoichiometric Elimination"
    Graduated: December 2010. Download project pdf here .
  17. Brett Bozyk
    Master's Thesis: "Nonanalytic Singular Continuations of Complex Analytic Dynamical Systems"
    Graduated: July 2012. Download thesis pdf here .
  18. Sarah Kabes
    Master's Project: "The Transition between the Henon Map and the Complex Quadratic Map"
    Graduated: August 2012. Download project pdf here .
  19. Evan Oman
    Master's Project: "Infinite Levels of Complexity in a Family of One-Dimensional Singular Dynamical Systems"
    Graduated: August 2015. Download project pdf file here .
  20. Erik Peterson
    Master's Project: "An Application of Fractal Analysis and Wearable Tech to the Health of the Heart"
    Graduated: August 2015. Download project pdf file here .
  21. Soleh Dib
    Master's Project: "Generalized Chimera States in Two Interacting Populations of Kuramoto Oscillators"
    Graduated: Jan. 2016. Download project pdf file here .
  22. Vaclav Hasenohrl
    Master's Project: "Modeling of Ebola Control Strategies"
    (Coadvised with Harlan Stech.)
    Graduated: May 2016. Download project pdf file here .
  23. Yujiong Liu
    Master's Project: "A Connection between Analytic and Nonanalytic Singular Perturbations of the Quadratic Map: A Case Study"
    Graduated: May 2017. Download project pdf file here .
  24. Joseph Kell
    Master's Project: "The breakup and continuation of invariant circles"
    Graduated: December 2017. Download project pdf file here .
  25. Noah Wong
    Master's Project: "Newton's method for a nonanalytic perturbation of z^2-1"
    Expected Graduation: 2020.

Undergraduate Students

  1. Zbigniew Wdowiak
    UROP project: "Newton's method for cubics"
  2. Ron Nelson
    UROP project: "Computing Fractal Basin Boundaries"
  3. Eric Nielsen
    Research Assistant project: "Developing a GUI for a Dynanmical Systems Software Package (TBC)"
  4. Mircea Ungureanu
    UROP project: "Nonlinear Dynamics Applied to Financial Markets"
  5. Tim Luthens
    Research Assistant project: "Computing the Topology of `folded' Surfaces"
  6. Mike Dvorak
    UROP project: "Use of Dynamical Systems to Control Micoorganism Populations"
  7. Brian Ketelboeter
    UROP project: "The Cusp bifurcation in two dimensions"
  8. Dan Gastler
    UROP project: "The n-body problem"
    2000. (coadvised with Guihua Fei)
  9. Joseph Erickson, "Dynamical Systems software development", Research Assistant project, 2003-4.
  10. J P McBride
    UROP project: "Dynamical Systems Software"
  11. Seth Slettedahl
    UROP project: "The dynamics of a noninvertible 2D map"
  12. Heather Chopp
    UROP project: Harvesting in a 2-D Producer/Consumer Model
  13. Jerod Lass
    Honors Project: "Analysis of Traffic Circles"
  14. Jacob Yunker
    Honors Project: "Statistical analysis for a proposed mechanism of protein-membrane interactions"
  15. Brett Bozyk
    Honors Project: "The spine of Newton's Method for Cubics"
  16. Brock Burgau
    UROP/Honors Project: "Water Treatment and Pollution in Lake Superior"
  17. Thomas Cameron
    UROP/Honors Project: "Dynamics of Newton's Method: a family of Quartic Polynomials"
  18. Jordan Maiers
    UROP/Honors Project: "Singular Perturbations of the quadratic map: z^2+c+B/zbar^2"
    Download pdf file here .
  19. Xinsheng Zhang, "The effect of hospital bed limitation on the spread of Ebola,"
    UROP and Honors Project
    May 2015. Download here .
  20. Haitao Shang
    Independent Study/Honors Project: "The Dynamics of [perturbations of] quadratic maps"
    2015. Download from here.
  21. Matthew Arthur
    UROP/Honors Project: "Perturbing z^2+c with a moving singularity"
    Download pdf file for BP-edited 2019 version here . 2015.
  22. Lesheng Wang
    UROP/Honors Project: Dynamics of a Singularly perturbed quadratic family
    (z2+c+B/zbar^d with d=1 or 2) 2017. Download pdf file for BP-edited 2019 version here .
  23. Patrick Andresen
    Honors Project: "Analyzing the Dynamics of z^2+0.1(t/z+(1-t)/zbar)
  24. Michael Wroblewski
    Honors project: "Perturbed Quadratic maps: Transition from annalytic to non-analytic: f(z)=z^2+0.09(t/z^3+(1-t)/zbar^3)"
  25. Blake Shoemaker
    UROP project: "Reversing the escape algorithm in the plane"
    2020. Download pdf here. Link to paper posted on UMN Digital Conservancy here .

This page is maintained by Bruce Peckham ( and was last modified on Saturday, 30-May-2020 09:25:26 CDT.