Ruan, Shigui; Wei, Junjie On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion. (English) Zbl 0982.92008 IMA J. Math. Appl. Med. Biol. 18, No. 1, 41-52 (2001). Summary: 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. Cited in 111 Documents MSC: 92C30 Physiology (general) 34K60 Qualitative investigation and simulation of models involving functional-differential equations 34K20 Stability theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations 92C50 Medical applications (general) 93C95 Application models in control theory Keywords:delay differential equation; exponential polynomial; control of testosterone secretion; steady state; Hopf bifurcation PDFBibTeX XMLCite \textit{S. Ruan} and \textit{J. Wei}, IMA J. Math. Appl. Med. Biol. 18, No. 1, 41--52 (2001; Zbl 0982.92008)