Weakly nonlinear optimal perturbations

Nonlinear optimal perturbations in a Couette flow: bursting and transition

Optimal waveform for fast entrainment of weakly forced nonlinear oscillators.

For many biological and engineered systems, a central function or design goal is to abbreviate the time required to synchronize a rhythmic process to an external forcing signal. We present a theory for deriving the input that effectively minimizes the average transient time required to entrain a phase model, which enables a practical technique for constructing fast entrainment waveforms for gen...

Conditional nonlinear optimal perturbations as the optimal precursors for El Nino–Southern Oscillation events

[1] We used the approach of conditional nonlinear optimal perturbation (CNOP) to investigate optimal precursors for El Nino–Southern Oscillation (ENSO) events with a theoretical coupled ocean-atmosphere model. The CNOPs of the annual cycle of the coupled system were computed for different time periods, and the derived CNOPs were compared with the linear singular vectors (LSVs). The results show...

Noise Perturbations of Nonlinear Dynamical

We investigate analytical methods to predict the long-time cumulative eects of noise perturbations on nonlinear dynamical systems. The study of such perturbations addresses the problem of the global stability of nonlinear systems with multiple coexisting attractors. Indeed small random perturbations can cause large excursions of the system from a nominal steady state, and hence induce transitio...

Weakly nonlinear internal gravity wavepackets

Horizontally periodic, vertically localized internal wavepackets evolve nonlinearly due only to interactions between the waves and their wave-induced mean flow. The corresponding weakly nonlinear equation that describes the evolution of the amplitude envelope before the onset of parametric subharmonic instability is examined. The results are compared with fully nonlinear numerical simulations a...