Bifurcation analysis in a scalar delay differential equation. (English) Zbl 1141.34045

Wei, Junjie

Nonlinearity 20, No. 11, 2483-2498 (2007).

The equations
\[ \dot {p}(t) = \frac{\beta \theta ^n}{\theta ^n + p^n(t - \tau )} - \gamma p(t),\quad t \geq 0 \]
and
\[ \dot {p}(t) = \frac{\beta \theta ^np^n(t - \tau )}{\theta ^n + p^n(t - \tau )} - \gamma p(t), \quad t \geq 0 \] describing the physiological control system are considered. Using normal form and center manifold techniques and global Andronov-Hopf bifurcation results by J. Wu [Trans. Am. Math. Soc. 350, 4799–4838 (1998; Zbl 0905.34034)] global existence of multiple periodic solutions is proved.

Reviewer: Boris V. Loginov (Ul’yanovsk)

MSC:

34K18	Bifurcation theory of functional-differential equations
92C35	Physiological flow

Keywords:

nonlinear ODE; delay; Andronov-Hopf bifurcation; global existence of periodic solutions

Citations:

Zbl 0905.34034