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Bifurcation analysis on a survival red blood cells model. (English) Zbl 1105.34047
The paper considers a scalar delay differential equation of the form \[ \dot u (t)=-\sigma u(t)+\exp(-u(t-\nu)), \] depending on the two positive parameters \(\sigma\) and \(\nu\). First, the authors find a sequence of critical values \(\nu_k\) for which the unique equilibrium undergoes a supercritical Hopf bifurcation.
Then, the authors apply J. Wu’s degree theoretical result [Trans. Am. Math. Soc. 350, No. 12, 4799–4838 (1998; Zbl 0905.34034)] to show that the periodic solutions emanating from the Hopf bifurcation continue to exist for all \(\nu\in(\nu_k,\infty)\). Having the paper of Wu at hand is recommended because the notation in the degree theoretical part of the paper is not self-contained.

MSC:
34K18 Bifurcation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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