An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations

Details An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations

2007-04-28

arxiv.org/abs/0704.3820v1

Comptes Rendus Mathematique, Volume 345, Issue 10, 15 November 2007, Pages 549-554

Mathematics

Spectral Theory

7 pages, in English, with an abridged French version

Scientific paper

10.1016/j.crma.2007.10.001

For monotone linear differential systems with periodic coefficients, the (first) Floquet eigenvalue measures the growth rate of the system. We define an appropriate arithmetico-geometric time average of the coefficients for which we can prove that the Perron eigenvalue is smaller than the Floquet eigenvalue. We apply this method to Partial Differential Equations, and we use it for an age-structured systems of equations for the cell cycle. This opposition between Floquet and Perron eigenvalues models the loss of circadian rhythms by cancer cells.

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