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Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs. (English) Zbl 1311.34123
Summary: 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.

34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34C12 Monotone systems involving ordinary differential equations
15B48 Positive matrices and their generalizations; cones of matrices
34A30 Linear ordinary differential equations and systems
34F05 Ordinary differential equations and systems with randomness
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