asynchronous exponential growth
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Author(s):  
Ryszard Rudnicki ◽  
Katarzyna Pichór

We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive operators we establish new criteria for an asynchronous exponential growth of solutions to such equations. We discuss the question of exponential size growth of cells. We show how to incorporate into our description models with constant increase of size and with target size division. We also present versions of the model when the population is heterogeneous.


2017 ◽  
Vol 27 (03) ◽  
pp. 1750032 ◽  
Author(s):  
Dongxue Yan ◽  
Xianlong Fu

This paper is devoted to the study of a spatially and size-structured population dynamics model with delay in the birth process. We investigate some dynamical properties of the equation by using [Formula: see text]-semigroup theory and spectral analysis arguments, through which we obtain some sufficient conditions of asymptotical stability, asynchronous exponential growth at the null equilibrium as well as Hopf bifurcation occurring at the positive steady state of the system. Some examples are presented and simulated to illustrate the obtained results.


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