13 citations · 45 across the 7 of their papers we have counts for
8 papers
The Lorenz system as a gradient-like system
Jeremy P Parker
We formulate, for continuous-time dynamical systems, a sufficient condition to be a gradient-like system, i.e. that all bounded trajectories approach stationary points and therefor…
Predicting chaotic statistics with unstable invariant tori
Jeremy P. Parker, Omid Ashtari, Tobias M. Schneider
It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic…
Koopman analysis of the periodic Korteweg-de Vries equation
Jeremy P Parker, Claire Valva
The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoida…
Invariant tori in dissipative hyperchaos
Jeremy P Parker, Tobias M Schneider
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's c…
A study of the double pendulum using polynomial optimization
Jeremy P Parker, David Goluskin, Geoffrey M Vasil
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtain…
The viscous Holmboe instability for smooth shear and density profiles
Jeremy P. Parker, Colm-cille P. Caulfield, Rich R. Kerswell
The Holmboe wave instability is one of the classic examples of a stratified shear instability, usually explained as the result of a resonance between a gravity wave and a vorticity…
Kelvin-Helmholtz billows above Richardson number
J. P. Parker, C. P. Caulfield, R. R. Kerswell
We study the dynamical system of a forced stratified mixing layer at finite Reynolds number , and Prandtl number . We consider a hyperbolic tangent background velocity pr…
Koopman analysis of isolated fronts and solitons
Jeremy Parker, Jacob Page
A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyse non…