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

Abstract

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.

arXiv comment7 pages, in English, with an abridged French version

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• Self-similarity in a General Aggregation-Fragmentation Problem ; Application to Fitness Analysis
• Non-linear eigenvalue problems arising from growth maximization of positive linear dynamical systems