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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Stability analysis of a simplified model for the control of testosterone secretion

Pages: 729 - 738, Volume 4, Issue 3, August 2004      doi:10.3934/dcdsb.2004.4.729

 
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Hongshan Ren - Department of Mathematics, Heilongjiang University, Harbin, 150080, China (email)

Abstract: In [1] a simplified model for the control of testosterone secretion is given by

$ \frac{dR}{dt}=f(T)-b_1R,\qquad\qquad\qquad\qquad $(*)

$ \frac{dT}{dt}=b_2R(t-\tau)-b_3T, $

where $R$ denotes the luteinizing hormone releasing hormone, $T$ denotes the hormone testosterone and the negative feedback function $f(T)$ is a positive monotonic decreasing differentiable function of $T$. The delay $\tau$ is associated with the blood circulation time in the body, and $b_1$, $b_2$ and $b_3$ are positive parameters. In this paper, developing the method given in [2], we establish necessary and sufficient conditions for the steady state of (*) to be asymptotic stable or linearly unstable.

Keywords:  Mathematical model, stability, linearly unstable, hormone.
Mathematics Subject Classification:  34K20, 34C25.

Received: November 2002;      Revised: February 2004;      Available Online: May 2004.