Peter Ashwin
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View article: Chaotic variability in a model of coupled ice streams
Chaotic variability in a model of coupled ice streams Open
Regions of fast-flowing ice in ice sheets, known as ice streams, have been theorized to be able to exhibit build-up/surge oscillatory variability due to thermomechanical coupling at the base of the ice. A simple model of three coupled ice …
View article: Early warning skill, extrapolation and tipping for accelerating cascades
Early warning skill, extrapolation and tipping for accelerating cascades Open
We investigate how nonlinear behaviour (both of forcing in time and of the system itself) can affect the skill of early warning signals (EWS) to predict tipping in (directionally) coupled bistable systems when using measures based on criti…
View article: Construction of invariant curves for some piecewise isometries
Construction of invariant curves for some piecewise isometries Open
View article: Attracting measures
Attracting measures Open
Under mild assumptions, the SRB measure $μ$ associated to an Axiom A attractor $A$ has the following properties: (i) the empirical measure starting at a typical point near $A$ converges weakly to $μ$; (ii) the pushforward of any Lebesgue-a…
View article: Early warning skill, extrapolation and tipping for accelerating cascades
Early warning skill, extrapolation and tipping for accelerating cascades Open
We investigate how nonlinear behaviour (both of forcing in time and of the system itself) can affect the skill of early warning signals to predict tipping in (directionally) coupled bistable systems when using measures based on critical sl…
View article: The effect of timescale separation on the tipping window for chaotically forced systems
The effect of timescale separation on the tipping window for chaotically forced systems Open
Tipping behaviour can occur when an equilibrium loses stability in response to a slowly varying parameter crossing a bifurcation threshold, or where noise drives a system from one attractor to another, or some combination of these effects.…
View article: Return-time and pullback-convergence properties of statistical attractors
Return-time and pullback-convergence properties of statistical attractors Open
Various definitions of an attractor for a nonlinear dynamical system have been proposed. These use various assumptions on the set of initial conditions that should converge (the basin), and various notions of convergence. A weak assumption…
View article: Beyond the loss of beta cells: a quantitative analysis of islet architecture in adults with and without type 1 diabetes
Beyond the loss of beta cells: a quantitative analysis of islet architecture in adults with and without type 1 diabetes Open
Aims/hypothesis The organisation and cellular architecture of islets of Langerhans are critical to the physiological regulation of hormone secretion but it is debated whether human islets adhere to the characteristic mantle–core (M-C) stru…
View article: Global Bifurcations Organizing Weak Chimeras in Three Symmetrically Coupled Kuramoto Oscillators with Inertia
Global Bifurcations Organizing Weak Chimeras in Three Symmetrically Coupled Kuramoto Oscillators with Inertia Open
Frequency desynchronized attractors cannot appear in identically coupled symmetric phase oscillators because “overtaking" of phases cannot occur. This restriction no longer applies for more general identically coupled oscillators. Hence, i…
View article: Quantifying tipping behavior: Geometric early warnings and quasipotentials for a box model of AMOC
Quantifying tipping behavior: Geometric early warnings and quasipotentials for a box model of AMOC Open
A non-autonomous system can undergo a rapid change of state in response to a small or slow change in forcing, due to the presence of nonlinear processes that give rise to critical transitions or tipping points. Such transitions are thought…
View article: Contrasting Chaotic and Stochastic Forcing: Tipping Windows and Attractor Crises
Contrasting Chaotic and Stochastic Forcing: Tipping Windows and Attractor Crises Open
This is the author accepted manuscript. The final version is available from the Society for Industrial and Applied Mathematics via the DOI in this record
View article: A Novel Route to Oscillations via non-central SNICeroclinic Bifurcation: Unfolding the Separatrix Loop Between a Saddle-Node and a Saddle
A Novel Route to Oscillations via non-central SNICeroclinic Bifurcation: Unfolding the Separatrix Loop Between a Saddle-Node and a Saddle Open
In this paper, we investigate saddle-node to saddle separatrix--loops that we term SNICeroclinic bifurcations. They are generic codimension-two bifurcations involving a heteroclinic loop between one non-hyperbolic and one hyperbolic saddle…
View article: Deep learning for predicting rate-induced tipping
Deep learning for predicting rate-induced tipping Open
Nonlinear dynamical systems exposed to changing forcing values can exhibit catastrophic transitions between distinct states. The phenomenon of critical slowing down can help anticipate such transitions if caused by a bifurcation and if the…
View article: Transients versus network interactions give rise to multistability through trapping mechanism
Transients versus network interactions give rise to multistability through trapping mechanism Open
In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients t…
View article: Internal Noise Interference to Warnings of Tipping Points in Generic Multidimensional Dynamical Systems
Internal Noise Interference to Warnings of Tipping Points in Generic Multidimensional Dynamical Systems Open
This is the author accepted manuscript. The final version is available from the Society for Industrial and Applied Mathematics via the DOI in this record
View article: Quantifying risk of a noise-induced AMOC collapse from northern and tropical Atlantic Ocean variability
Quantifying risk of a noise-induced AMOC collapse from northern and tropical Atlantic Ocean variability Open
The Atlantic Meridional Overturning Circulation (AMOC) exerts a major influence on global climate. There is much debate about whether the current strong AMOC may collapse as a result of anthropogenic forcing and/or internal variability. In…
View article: Emergence and stability of endoplasmic reticulum network streaming in plant cells
Emergence and stability of endoplasmic reticulum network streaming in plant cells Open
View article: Deep Learning for predicting rate-induced tipping
Deep Learning for predicting rate-induced tipping Open
Nonlinear dynamical systems exposed to changing forcing can exhibit catastrophic transitions between alternative and often markedly different states. The phenomenon of critical slowing down (CSD) can be used to anticipate such transitions …
View article: Arbitrary sensitive transitions in recurrent neural networks
Arbitrary sensitive transitions in recurrent neural networks Open
This is the final version. Available on open access from Elsevier via the DOI in this record
View article: On the predictability of possible storylines for forced complex systems
On the predictability of possible storylines for forced complex systems Open
It is well-known that even for fairly simple deterministic nonlinear systems, exact prediction of future state is, on average, impossible beyond some small multiple of the Lyapunov time that quantifies the rate of separation of trajectorie…
View article: Global bifurcations organizing weak chimeras in three symmetrically coupled Kuramoto oscillators with inertia
Global bifurcations organizing weak chimeras in three symmetrically coupled Kuramoto oscillators with inertia Open
Frequency desynchronized attractors cannot appear in identically coupled symmetric phase oscillators because "overtaking" of phases cannot occur. This restriction no longer applies for more general identically coupled oscillators. Hence, i…
View article: Renormalization of translated cone exchange transformations
Renormalization of translated cone exchange transformations Open
In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a geometr…
View article: AMOC stability amid tipping ice sheets: the crucial role of rate and noise
AMOC stability amid tipping ice sheets: the crucial role of rate and noise Open
The Atlantic Meridional Overturning Circulation (AMOC) has recently been categorized as a core tipping element as, under climate change, it is believed to be prone to critical transition implying drastic consequences on a planetary scale. …
View article: Transitions in echo index and dependence on input repetitions
Transitions in echo index and dependence on input repetitions Open
The echo index counts the number of simultaneously stable asymptotic responses of a nonautonomous (i.e. input-driven) dynamical system. It generalises the well-known echo state property for recurrent neural networks — this corresponds to t…
View article: Contrasting chaotic and stochastic forcing: tipping windows and attractor crises
Contrasting chaotic and stochastic forcing: tipping windows and attractor crises Open
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are sma…
View article: A Continuous Time Dynamical Turing Machine
A Continuous Time Dynamical Turing Machine Open
Continuous time recurrent neural networks (CTRNNs) are systems of coupled ordinary differential equations (ODEs) inspired by the structure of neural networks in the brain. CTRNNs are known to be universal dynamical approximators: given a l…
View article: Characterising Edge States: Measures on chaotic non-attracting invariant sets
Characterising Edge States: Measures on chaotic non-attracting invariant sets Open
In this work, we explore how to extend the concept of physical measures from attractors to chaotic non-attracting invariant sets. Building on Sweet and Ott’s work from 2000, we make their ideas rigorous by defining a measure on non-a…
View article: AMOC Stability amid Tipping Ice Sheets from Conceptual to Intermediate Complexity Models
AMOC Stability amid Tipping Ice Sheets from Conceptual to Intermediate Complexity Models Open
The Atlantic Meridional Overturning Circulation (AMOC) and polar ice sheets are considered susceptible to critical transitions under climate change. Identified as core tipping elements, their collapse would have global and drastic conseque…
View article: Quantifying risk of a noise-induced AMOC collapse from northern and tropical Atlantic Ocean variability
Quantifying risk of a noise-induced AMOC collapse from northern and tropical Atlantic Ocean variability Open
The Atlantic Meridional Overturning Circulation (AMOC) exerts a major influence on global climate. There is much debate about whether the current strong AMOC may collapse as a result of anthropogenic forcing and/or natural variability. Her…
View article: Anticipating rate-induced tipping by a deep learning framework
Anticipating rate-induced tipping by a deep learning framework Open
Rate-induced tipping (R-tipping) occurs when the forcing rate changes too rapidly for the system to track its quasi-equilibrium state, leading to an unexpected collapse. Currently, there is a lack of valid early warning signals (EWS) for R…