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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.

MSC:
 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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