Related papers: Attractors and bifurcation diagrams in complex cli…
Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…
It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case we present a scheme of analysis that…
The climate is a non-equilibrium system undergoing the continuous action of forcing and dissipation. Under the effect of a spatially inhomogeneous absorption of solar energy, all the climate components dynamically respond until an…
We apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity climate model and analyze their interplay. First, drawing from the theory of quasipotentials, and viewing the state space as…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
Multistability is a ubiquitous feature in systems of geophysical relevance and provides key challenges for our ability to predict a system's response to perturbations. Near critical transitions small causes can lead to large effects and -…
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a…
Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as…
The first step in exploring the properties of dynamical systems like the Earth climate is to identify the different phase space regions where the trajectories asymptotically evolve, called `attractors'. In a given system, multiple…
The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…
Low-order climate models can play an important role in understanding low-frequency variability in the atmospheric circulation and how forcing consistent with anthropogenic climate change may affect this variability. Here, we study a…
Using in a simple way the theory of non linear dynamical systems, we show that increasing climatic instabilities may be a qualitative warning sign for the occurrence of a nearby bifurcation, yielding a discontinuous and sudden climate…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…
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 climate models, which are piecewise-smooth continuous…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Models of complex dynamical systems like the Earth's climate often involve large numbers of uncertain parameters. Comprehensive exploration of the parameter space is typically prohibitive due to excessive computational costs. Systematic…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
Current techniques for predicting climate change are mainly based on "massive" deterministic numerical modeling. However, the ocean-atmosphere system is a so-called "complex system", made up of a large number of interacting elements. We…