Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs

TL;DR

This paper introduces a new method using polynomial Lyapunov-like functions to derive lower bounds for the top Lyapunov exponent in cooperative random linear ODE systems, extending classical eigenvalue estimates.

Contribution

It presents a novel approach for estimating the top Lyapunov exponent in cooperative systems, generalizing classical eigenvalue bounds.

Findings

New lower estimates for the top Lyapunov exponent

Extension of Frobenius and Kolotilina eigenvalue estimates

Application of polynomial Lyapunov functions to random systems

Abstract

For cooperative random linear systems of ordinary differential equations a method is presented of obtaining lower estimates of the top Lyapunov exponent. The proofs are based on applying some polynomial Lyapunov-like function. Known estimates for the dominant eigenvalue of a nonnegative matrix due to G. Frobenius and L. Yu. Kolotilina are shown to be specializations of our results.