# American Institute of Mathematical Sciences

August  2004, 4(3): 729-738. doi: 10.3934/dcdsb.2004.4.729

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

 1 Department of Mathematics, Heilongjiang University, Harbin, 150080, China

Received  November 2002 Revised  February 2004 Published  May 2004

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.

Citation: Hongshan Ren. Stability analysis of a simplified model for the control of testosterone secretion. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 729-738. doi: 10.3934/dcdsb.2004.4.729
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