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Characterization of intermittency at the onset of turbulence in the forced and damped nonlinear Schrödinger equation. (English) Zbl 07257100
Summary: In this paper we characterized intermittent transitions from temporal chaos to turbulence in the forced and damped nonlinear Schrödinger equation. We demonstrate using finite time Lyapunov exponents that during the transition a fraction of unstable periodic orbits embedded in a low dimensional chaotic attractor loses transversal stability, in a way that nearby trajectories are expelled away from its vicinity (a mechanism referred to as intermittency induced by Unstable Dimension Variability). During the transition, an appropriate decomposition of the Fourier phase space into transversal and longitudinal modes is performed. The analysis of modes dynamics sheds new light in the understanding of intermittency in spatially extended dynamical systems. Subsequently a perturbation is applied to the system in order to control the intermittent extreme events and reduce their occurrence.
MSC:
37 Dynamical systems and ergodic theory
70 Mechanics of particles and systems
Software:
LSODE
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