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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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Estimates for Principal Lyapunov Exponents: A Survey

Janusz Mierczyński
  • Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, PL-50-370 Wrocław, Poland
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Published Online: 2014-11-12 | DOI: https://doi.org/10.2478/msds-2014-0008


This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself. Extensions to other differential equations are considered. Possible directions of further research are hinted.

Keywords: Principal Lyapunov exponent; principal spectrum; nonautonomous dynamical system; random dynamical system; upper and lower estimate; time-averaging; strongly cooperative system of ordinary differential equations; dominant eigenvalue; parabolic partial differential equation; principal eigenvalue; permanence


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About the article

Received: 2014-03-17

Accepted: 2014-09-01

Published Online: 2014-11-12

Citation Information: Nonautonomous Dynamical Systems, ISSN (Online) 2299-3193, DOI: https://doi.org/10.2478/msds-2014-0008.

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© 2014 Janusz Mierczyński. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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