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arXiv · 2301.06504

Bifurcation theory for SPDEs: finite-time Lyapunov exponents and amplitude equations

Dirk Blömker·Alexandra Neamtu
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Abstract

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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Dirk Blömker, Alexandra Neamtu. 2023-01-16. Bifurcation theory for SPDEs: finite-time Lyapunov exponents and amplitude equations. https://arxiv.org/abs/2301.06504

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