688 citations · 3.2k across the 69 of their papers we have counts for
9 papers · 1 filter
Choosing observables that capture critical slowing down before tipping points: A Fokker-Planck operator approach
Johannes Lohmann, Georg A. Gottwald
Tipping points (TP) are abrupt transitions between metastable states in complex systems, most often described by a bifurcation or crisis of a multistable system induced by a slowly…
Edgeworth expansions for slow-fast systems with finite time scale separation
Jeroen Wouters, Georg A. Gottwald
We derive Edgeworth expansions that describe corrections to the Gaussian limiting behaviour of slow-fast systems. The Edgeworth expansion is achieved using a semi-group formalism f…
On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series
Georg A. Gottwald, Caroline L. Wormell, Jeroen Wouters
Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-…
On finite-size Lyapunov exponents in multiscale systems
Lewis Mitchell, Georg A. Gottwald
We study the effect of regime switches on finite size Lyapunov exponents (FSLEs) in determining the error growth rates and predictability of multiscale systems. We consider a dynam…
On the Implementation of the 0-1 Test for Chaos
Georg A. Gottwald, Ian Melbourne
In this paper we address practical aspects of the implementation of the 0-1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which sig…
On the Validity of the 0-1 Test for Chaos
Georg A. Gottwald, Ian Melbourne
In this paper, we present a theoretical justification of the 0-1 test for chaos. In particular, we show that with probability one, the test yields 0 for periodic and quasiperiodic…