Local Lyapunov Exponents: Sublimiting Growth Rates of Linear Random Differential Equations

✍ Scribed by Wolfgang Siegert (auth.)

• Book ID: 127454837
• Publisher: Springer
• Year: 2009
• Tongue: English
• Weight: 2 MB
• Edition: 1
• Category: Library
• City: Berlin
• ISBN-13: 9783540859635
• DOI: 10.1007/978-3-540-85964-2

✦ Synopsis

Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations.
Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.

✦ Subjects

Genetics and Population Dynamics