PMID: 11339337May 8, 2001Paper

On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion

IMA Journal of Mathematics Applied in Medicine and Biology
Shigui Ruan, J Wei

Abstract

In this paper, we first study the distribution of the zeros of a third degree exponential polynomial. Then we apply the obtained results to a delay model for the control of testosterone secretion. It is shown that under certain assumptions on the coefficients the steady state of the delay model is asymptotically stable for all delay values. Under another set of conditions, there is a critical delay value, the steady state is stable when the delay is less than the critical value and unstable when the delay is greater than the critical value. Thus, oscillations via Hopf bifurcation occur at the steady state when the delay passes through the critical value. Numerical simulations are presented to illustrate the results.

Citations

Nov 7, 2006·Bulletin of Mathematical Biology·Mostafa AdimyShigui Ruan
Oct 14, 2004·Journal of Mathematical Biology·German Enciso, Eduardo D Sontag
Dec 2, 2009·IET Systems Biology·F XuR Wang
Sep 2, 2008·Mathematical Biosciences·Fabien CrausteAbdelaziz Kacha
Nov 10, 2015·Journal of Theoretical Biology·G NeofytouK B Blyuss
May 10, 2008·IEEE Transactions on Neural Networks·Wenwu YuGuanrong Chen
Feb 10, 2006·Mathematical Biosciences·Liancheng Wang, Michael Y Li
Feb 7, 2015·Journal of Mathematical Biology·Hongying ShuJames Watmough
Jul 28, 2016·SpringerPlus·Mehbuba RehimAhmadjan Muhammadhaji

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