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Talk Abstract
Chaotic Behavior of a Model of the Hypothalamo-Pituitary-Gonad Axis in Man

Bingzheng Liu
Department of Physics
Northeast Normal University
Changchun, 130024

We propose a nonlinear dynamical model for the pulsatile secretion of the hypothalamo-pituitary-gonad axis in man. The system of differential equations involves five variables--plasma concentrations of GnRH(LRH), LH, free testosterone, TEBG-bound testosterone and albumin-bound testosterone. The equations are solved by means of fourth-order Runge-Kutta method. The resulted time evolution curves, the bifurcation diagrams, the return maps and the Lyapunov exponents all strongly indicate that we have chaotic solutions. We believe chaotic solutions agree with the pulsatile pattern better than periodic solutions, and consistent with the excellent observations and analysis of Prank on parathyroid hormone. Some other results from the model, including basal concentrations, production rates and MCR, etc. also agree well with experimental results.

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1998-1999 Mathematics in Biology
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