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

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.

MSC:

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

Citations:

Zbl 0905.34034
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