28 citations · 38 across the 4 of their papers we have counts for
5 papers
An early warning system for multivariate time series with sparse and non-uniform sampling
Andrew Roberts, Sasanka Are
In this paper we propose a new early warning test statistic, the ratio of deviations (RoD), which is defined to be the root mean squared of successive differences divided by the st…
Detecting transient rate-tipping using Steklov averages and Lyapunov vectors
Alanna Hoyer-Leitzel, Alice Nadeau, Andrew Roberts +1
A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In…
Persistence of Saddle Behavior in the Nonsmooth Limit of Smooth Dynamical Systems
Julie Leifeld, Kaitlin Hill, Andrew Roberts
Models such as those involving abrupt changes in the Earth's reflectivity due to ice melt and formation often use nonlinear terms (e.g., hyperbolic tangent) to model the transition…
Canard explosion and relaxation oscillation in planar, piecewise-smooth, continuous systems
Andrew Roberts
Classical canard explosion results in smooth systems require the vector field to be at least , since canard cycles are created as the result of a Hopf bifurcation. The work on…
Canard-like phenomena in piecewise-smooth Van der Pol systems
Andrew Roberts, Paul Glendinning
We show that a nonlinear, piecewise-smooth, planar dynamical system can exhibit canard phenomena. Canard solutions and explosion in nonlinear, piecewise-smooth systems can be quali…