My current research is focused on two areas: (1) modelling the estrogen (menstrual) cycle in humans to study cycle abnormalities, and (2) the use of
stocking, harvesting and migration to control the dynamical behavior of deterministic models in population biology and genetics.
Angelean O. Hendrix and James F. Selgrade (2014). Bifurcation analysis of a menstrual cycle model reveals multiple mechanisms linking testosterone and classical PCOS. J. Theoretical Biology 361, 31-40.
Angelean O. Hendrix, Claude L. Hughes and James F. Selgrade (preprint). (2014) Modeling endocrine control of the pituitary-ovarian axis: Androgenic influence and chaotic dynamics. Bull. Math. Biology 76, 136-156.
Alison Margolskee and James F. Selgrade (2013). A lifelong model for the female reproductive cycle with an antimullerian hormone treatment to delay menopause. J. Theoretical Biology 326, 21-35.
Alison Margolskee and James F. Selgrade (2011). Dynamics and bifurcation of a model for hormonal control of the menstrual cycle with inhibin delay, Math. Biosciences 234, 95-107.
James F. Selgrade (2010). Bifurcation analysis of a model for hormonal regulation of the menstrual cycle, Math. Biosciences 225, 97-103.
James F. Selgrade, L.A. Harris and R.D. Pasteur (2009). A model for hormonal control of the menstrual cycle: Structural consistency but sensitivity with regard to data, J. Theoretical Biology 260, 572-580.
James F. Selgrade, Jordan W. Bostic and James H. Roberds (2009). Dynamical behavior of a discrete selection-migration model with arbitrary dominance, Jour. of Difference Equations and Appl. 15, 371-385.
James F. Selgrade and James H. Roberds (2007). Global attractors for a discrete selection model with periodic immigration, Jour. of Difference Equations and Appl. 13, 275-287.
James F. Selgrade and James H. Roberds (2005). Results on asymptotic behavior for discrete, two-patch metapopulations with density-dependent selection, Jour. of Difference Equations and Appl. 11, 459-476.
John E. Franke and James F. Selgrade (2003). Attractors for discrete periodic dynamical systems, J. Math. Analysis and Applications 286, 64-79.
L. Harris Clark, Paul M. Schlosser and James F. Selgrade (2003). Multiple stable periodic solutions in a model for hormonal control of the menstrual cycle, Bulletin of Math. Biology 65, 157-173.
James F. Selgrade and James H. Roberds (2001). On the structure of attractors for discrete, periodically forced systems with applications to population models, Physica D 158, 69-82. Reprint
Paul M. Schlosser and James F. Selgrade (2000). A model of gonadotropin regulation during the menstrual cycle in women: Qualitative features, Environmental Health Perspectives 108(suppl 5), 873-881.
Title: Some Deterministic Models in Mathematical Biology and Their Simulations
Instructors: James F. Selgrade (North Carolina State University),
Cammey Cole (Meredith College)
and Huseyin Kocak (University of Miami)
This course presented and
analyzed the Hodgkin-Huxley and FitzHugh-Nagumo models, chemostat
models, pharmacokinetics models and discrete population models. The class was conducted in
a computer lab where participants used the software Phaser to simulate model behavior.
For details see www.phaser.com .
A similar MAA minicourse was held at Meredith College, March 2005.
For help with integrals see: http://integrals.wolfram.com
For on-line math courses see: on-line math
MA 537-001 textbook:
``A First Course in Chaotic Dynamical Systems'' by R.L. Devaney
MA 537 Course Policy & Information
Due Jan. 12: Information, p.2, # 1*, 2*, 3*;
Due Jan. 16: Information, p.3, # 4*, 5*;
Due Jan. 23: Newton Method*; p.26, #6, 8, 12*, 13*, 14*; Turn in starred problems only.
Due Jan. 30: p.50, #1 a*,b*,c*, 4 a, f*, g*, 5, 6, 7, 8, 9;
MA 537 Homework and Test Solutions
Some General Information on Policy for Mathematics Courses