Publikation: On the pitchfork bifurcation for the Chafee–Infante equation with additive noise
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We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor is a singleton, independently of the value of the bifurcation parameter; this phenomenon is often referred to as the “destruction” of the bifurcation by the noise. Analogous to the results of Callaway et al. (AIHP Prob Stat 53:1548–1574, 2017) for a 1D stochastic ODE, we show that some remnant of the bifurcation persists for this SPDE model in the form of a positive finite-time Lyapunov exponent. Additionally, we prove finite-time expansion of volume with increasing dimension as the bifurcation parameter crosses further eigenvalues of the Laplacian.
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BLUMENTHAL, Alex, Maximilian ENGEL, Alexandra BLESSING-NEAMTU, 2023. On the pitchfork bifurcation for the Chafee–Infante equation with additive noise. In: Probability Theory and Related Fields. Springer. 2023, 187(3-4), pp. 603-627. ISSN 0178-8051. eISSN 1432-2064. Available under: doi: 10.1007/s00440-023-01235-3BibTex
@article{Blumenthal2023pitch-69740, year={2023}, doi={10.1007/s00440-023-01235-3}, title={On the pitchfork bifurcation for the Chafee–Infante equation with additive noise}, number={3-4}, volume={187}, issn={0178-8051}, journal={Probability Theory and Related Fields}, pages={603--627}, author={Blumenthal, Alex and Engel, Maximilian and Blessing-Neamtu, Alexandra} }
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