Abstract
The author shows that Perron-Frobenius theorem is a valuable tool for the investigation of L-systems, as he deepens the analysis of growth functions of cell populations with lineage control, by means of suitable results proposed hereinafter. Among these results are conditions for ƒ(t),t=1,2,3,…, to be asymptotically equal to br t , where b is a constant and ƒ( t) is the growth function of the system generated by the nonnegative irreducible square matrix C with spectral radius r. The values of lim C t r r , lim ƒ(t+1) ƒ(t) , and lim ƒ(t) r t are given in terms of the coefficients of the eigenvalues of C in the analytical expression for ƒ( t). The technique of growth functions is shown to be an appropriate tool for the analysis of the above type of matrices, which are relevant in many fields of application.
Published Version
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