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- W1853114517 abstract "Let λ denote the almost sure Lyapunov exponent obtained by linearizing the stochastic Duffing-van der Pol oscillator $$ ddot{x} = - {w^{2}}x + beta dot{x} - A{x^{3}} - B{x^{2}}dot{x} + sigma x{dot{W}_{t}} $$at the origin x = x = 0 in phase space. If λ > 0 then the process {(x t , x t ): t > 0} is positive recurrent on R2 {(0,0)} with stationary probability measure μ, say. For λ > 0 let ( tilde{lambda } ) denote the almost sure Lyapunov exponent obtained by linearizing the same equation along a typical stationary trajectory in R 2 ∖{(0,0)}. The sign of ( tilde{lambda } ) is important for stability properties of the two point motion associated with the original equation. We use stochastic averaging techniques to estimate the value of ( tilde{lambda } ) in the presence of small noise and small viscous damping." @default.
- W1853114517 created "2016-06-24" @default.
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- W1853114517 date "2003-01-01" @default.
- W1853114517 modified "2023-09-27" @default.
- W1853114517 title "Lyapunov Exponents and Stability for the Stochastic Duffing-Van der Pol Oscillator" @default.
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- W1853114517 doi "https://doi.org/10.1007/978-94-010-0179-3_10" @default.
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