Erica J. Graham and James F. Selgrade (2017). A model of ovulatory regulation examining the effects of insulin-mediated testosterone production on ovulatory function, J. Theoretical Biology 416, 149-160.

Nicole M. Panza, A. A. Wright and J. F. Selgrade (2016). A delay differential equation model of follicle waves in women, Jour. of Biological Dynamics 10, 200-221.

Leona A. Harris and James F. Selgrade (2014). Modeling endocrine regulation of the menstrual cycle using delay differential equations, Math. Biosciences 257, 11-22.

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.