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. Research supported by NSF grants DMS-0920927 and DMS-1225607
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. Research supported by NSF grants DMS-0920927 and DMS-1225607
Alison Margolskee and J.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. http://dx.doi.org/10.1016/j.jtbi.2013.02.007 Research supported by NSF grants DMS-0920927 and DMS-1225607
Alison Margolskee and J.F. Selgrade. (2011). Dynamics and bifurcation of a model for hormonal control of the menstrual cycle with inhibin delay, Math. Biosciences 234, 95-107. http://dx.doi.org/10.1016/j.mbs.2011.09.001 Research supported by NSF grant DMS-0920927
James F. Selgrade (2010). Bifurcation analysis of a model for hormonal regulation of the menstrual cycle, Math. Biosciences 225, 97-103. http://dx.doi.org/10.1016/j.mbs.2010.02.004 Research supported by NSF grant DMS-0920927
Leona A. Harris and James F. Selgrade (2013). Modeling endocrine regulation of the menstrual cycle using delay differential equations, preprint
Decreasing the diameter of the cycle uniqueness interval as c_2 increases
An unfolding of a transcritical bifurcation as tau increases
A family of transcritical bifurcations as c_2 and tau vary