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Modelling and Simulation in Life and Material Sciences

Stability and existence boundaries of a Delay Equation for an age structured cell population dynamics

Yukihiko Nakata

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We present stability boundaries in a two-parameter plane for a Delay Equation (DE) for an age structured cell population dynamics. As two free parameters we choose mortality rate in the horizontal axis and maximum recruitment rate in the vertical axis. Increasing a weight of quiescent cell population that influences a transition mechanism, stability property changes. If the weight is sufficiently large there is a stability boundary which separates the existence region into the stability region and the instability region.

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As a third parameter we choose an age in which one cell divides to produce two daughter cells. As increasing the length, the shape of the stability region does not change dramatically. However, every curve where Hopf bifurcation occurs approaches the stability boundary.

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Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)