Figure 3
Limiting behaviour when \(t \rightarrow +\infty\) of a population with an initial number of cells, \(C_0 = 10^2\). Birth and death rates, \(\lambda\) and \(\mu\), have units of inverse time, \(t^{-1}\). Left: Parameters: \(N=5\), \(\lambda = 0.6\), \(\mu = (2^{1/N}-1)\lambda\). The population of cells in stage j levels out to \(2^{\frac{1-j}{N}} C_0/N\) for sufficiently large times. Centre: Parameters: \(N=5\), \(\lambda =0.5\), \(\mu = 0.1\). The population of cells at any stage becomes extinct at late times. Right: Parameters: \(N=5\), \(\lambda =0.8\), \(\mu =0.1\). The populations grow according to (3.11) and the relation between \(M_1\) and \(M_5\) given by Eq. (3.9) is satisfied. For example, at \(t=100\), \(M_1(t) \simeq 2^{4/5}M_5(t)\).
