Averaging in random systems of nonnegative matrices

Janusz  Mierczyński

doi:10.3934/proc.2015.0835

Article Contents

2015, Volume 2015: 835-840. Doi: 10.3934/proc.2015.0835 open access

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Averaging in random systems of nonnegative matrices

Janusz Mierczyński^1,

1.
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, PL-50-370 Wrocław

Received: July 31, 2014

Revised: March 31, 2015

Published: October 2015

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Abstract

It is proved that the top Lyapunov exponent of a random matrix system of the form $\{A D(\omega)\}$, where $A$ is a nonnegative matrix and $D(\omega)$ is a diagonal matrix with positive diagonal entries, is bounded from below by the top Lyapunov exponent of the averaged system. This is in contrast to what one should expect of systems describing biological metapopulations.

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Mathematics Subject Classification: Primary: 37H15, 15B48; Secondary: 92D25.

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