Estimates for Principal Lyapunov Exponents: A Survey

Janusz Mierczyński

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, Issue: 1, page 137-162, electronic only
  • ISSN: 2353-0626

Abstract

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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.

How to cite

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Janusz Mierczyński. "Estimates for Principal Lyapunov Exponents: A Survey." Nonautonomous Dynamical Systems 1.1 (2014): 137-162, electronic only. <http://eudml.org/doc/269442>.

@article{JanuszMierczyński2014,
abstract = {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.},
author = {Janusz Mierczyński},
journal = {Nonautonomous Dynamical Systems},
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; principal Lyapunov exponent; random dynamical system; strongly cooperative system of ordinary differential equations},
language = {eng},
number = {1},
pages = {137-162, electronic only},
title = {Estimates for Principal Lyapunov Exponents: A Survey},
url = {http://eudml.org/doc/269442},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Janusz Mierczyński
TI - Estimates for Principal Lyapunov Exponents: A Survey
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
IS - 1
SP - 137
EP - 162, electronic only
AB - 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.
LA - eng
KW - 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; principal Lyapunov exponent; random dynamical system; strongly cooperative system of ordinary differential equations
UR - http://eudml.org/doc/269442
ER -

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