# Estimates for Principal Lyapunov Exponents: A Survey

Nonautonomous Dynamical Systems (2014)

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

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topJanusz 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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