Abstract
This paper is devoted to the study of an age-cycle structured proliferating cell population with delayed boundary condition. Individual cells are distinguished by age and cell cycle length. We consider a general biological rule corresponding to delayed boundary condition. Our focus is on the asymptotic behavior of the system, in particular on the effect of the time lag on the long-term dynamics. To this end, within a semigroup framework, we derive the locally asymptotic stability and asynchrony results, respectively, for the considered population system under some conditions. For our discussion, we use operator matrices, Hille-Yosida operators, spectral analysis, as well as Perron-Frobenius theory.
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