43 citations · 150 across the 14 of their papers we have counts for
14 papers
Dynamic tipping and cyclic folds, in a one-dimensional non-smooth dynamical system linked to climate models
Chris Budd, Rachel Kuske
We study the behaviour at tipping points close to (smoothed) non-smooth fold bifurcations in one-dimensional oscillatory forced systems. The focus is the Stommel-Box, and related c…
WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming
Mengyi Tang, Wenjing Liao, Rachel Kuske +1
Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differenti…
Post-grazing dynamics of a vibro-impacting energy generator
Larissa Serdukova, Rachel Kuske, Daniil Yurchenko
The motion of a forced vibro-impacting inclined energy harvester is investigated in parameter regimes with asymmetry in the number of impacts on the bottom and top of the device. T…
Reduced α-stable dynamics for multiple time scale systems forced with correlated additive and multiplicative Gaussian white noise
William F. Thompson, Rachel A. Kuske, Adam. H. Monahan
Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has i…
The influence of localised randomness on regular grazing bifurcations with applications to impacting dynamics
David J. W. Simpson, Rachel Kuske
This paper concerns stochastic perturbations of piecewise-smooth ODE systems relevant for vibro-impacting dynamics, where impact events constitute the primary source of randomness.…
Tipping points near a delayed saddle node bifurcation with periodic forcing
Jielin Zhu, Rachel Kuske, Thomas Erneux
We consider the effect on tipping from an additive periodic forcing in a canonical model with a saddle node bifurcation and a slowly varying bifurcation parameter. Here tipping ref…
Stochastic averaging of dynamical systems with multiple time scales forced with α-stable noise
William F. Thompson, Rachel A. Kuske, Adam H. Monahan
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically…
Stochastic Perturbations of Periodic Orbits with Sliding
David J. W. Simpson, Rachel Kuske
Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a di…
Stochastic Regular Grazing Bifurcations
David J. W. Simpson, S. J. Hogan, Rachel Kuske
A grazing bifurcation corresponds to the collision of a periodic orbit with a switching manifold in a piecewise-smooth ODE system and often generates complicated dynamics. The lowe…
Stochastically Perturbed Sliding Motion in Piecewise-Smooth Systems
David J. W. Simpson, Rachel Kuske
Sliding motion is evolution on a switching manifold of a discontinuous, piecewise-smooth system of ordinary differential equations. In this paper we quantitatively study the effect…
The Positive Occupation Time of Brownian Motion with Two-Valued Drift and Asymptotic Dynamics of Sliding Motion with Noise
David J. W. Simpson, Rachel Kuske
We derive the probability density function of the positive occupation time of one-dimensional Brownian motion with two-valued drift. Long time asymptotics of the density are also c…
Dynamics of Simple Balancing Models with State Dependent Switching Control
David J. W. Simpson, Rachel Kuske, Yue-Xian Li
Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by ei…
Mixed-Mode Oscillations in a Stochastic, Piecewise-Linear System
David J. W. Simpson, Rachel Kuske
We analyze a piecewise-linear FitzHugh-Nagumo model. The system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist. The addition of small n…
Characterizing mixed mode oscillations shaped by noise and bifurcation structure
Peter Borowski, Rachel Kuske, Yue-Xian Li +1
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various m…