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Bifurcation Theory for SPDEs : Finite-time Lyapunov Exponents and Amplitude Equations

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2023

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Blömker, Dirk

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https://doi.org/10.1137/23m1549638
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SIAM Journal on Applied Dynamical Systems. Society for Industrial & Applied Mathematics (SIAM). 2023, 22(3), pp. 2150-2179. eISSN 1536-0040. Available under: doi: 10.1137/23m1549638

Zusammenfassung

We consider a stochastic partial differential equation close to bifurcation of pitchfork type, where a one-dimensional space changes its stability. For finite-time Lyapunov exponents we characterize regions depending on the distance from bifurcation and the noise strength where finite-time Lyapunov exponents are positive and thus detect bifurcations. One technical tool is the reduction of the essential dynamics of the infinite-dimensional stochastic system to a simple ordinary stochastic differential equation, which is valid close to the bifurcation.

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510 Mathematik

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finite-time Lyapunov exponents, amplitude equations, bifurcations of SPDEs

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ISO 690BLÖMKER, Dirk, Alexandra BLESSING-NEAMTU, 2023. Bifurcation Theory for SPDEs : Finite-time Lyapunov Exponents and Amplitude Equations. In: SIAM Journal on Applied Dynamical Systems. Society for Industrial & Applied Mathematics (SIAM). 2023, 22(3), pp. 2150-2179. eISSN 1536-0040. Available under: doi: 10.1137/23m1549638
BibTex
@article{Blomker2023Bifur-67990,
  year={2023},
  doi={10.1137/23m1549638},
  title={Bifurcation Theory for SPDEs : Finite-time Lyapunov Exponents and Amplitude Equations},
  number={3},
  volume={22},
  journal={SIAM Journal on Applied Dynamical Systems},
  pages={2150--2179},
  author={Blömker, Dirk and Blessing-Neamtu, Alexandra}
}
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