26 citations · 35 across the 6 of their papers we have counts for
6 papers
Numerical Computation of Quasiperiodic Reducible Saddle-Node Bifurcations: a Parameterization Method Approach
Jordi-Lluís Figueras, Joan Gimeno, Jeremy P. Parker
We present a method for computing reducible, normally hyperbolic, invariant tori with internal quasiperiodic dynamics in autonomous ordinary differential equation systems. The appr…
From synthetic turbulence to true solutions: A deep diffusion model for discovering periodic orbits in the Navier-Stokes equations
Jeremy P Parker, Tobias M Schneider
Generative artificial intelligence has shown remarkable success in synthesizing data that mimic complex real-world systems, but its potential role in the discovery of mathematicall…
Ghost states underlying spatial and temporal patterns: how non-existing invariant solutions control nonlinear dynamics
Zheng Zheng, Pierre Beck, Tian Yang +3
Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longe…
Data-driven guessing and gluing of unstable periodic orbits
Pierre Beck, Jeremy P. Parker, Tobias M. Schneider
Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatio-temporal chaos and turbulence. Finding these UPOs is however notoriously difficult.…
The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation
Marie Abadie, Pierre Beck, Jeremy P. Parker +1
The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, fo…
Variational methods for finding periodic orbits in the incompressible Navier-Stokes equations
Jeremy P Parker, Tobias M Schneider
Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such…