Bifurcation theory for SPDEs: finite-time Lyapunov exponents and amplitude equations. (English) Zbl 1526.37067
Summary: 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.
MSC:
| 37H20 | Bifurcation theory for random and stochastic dynamical systems |
| 37L55 | Infinite-dimensional random dynamical systems; stochastic equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
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