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The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions…
Understanding how climate and innovation policies perform during socio-technical transitions remains a central challenge in innovation studies. Empirical analyses of the relationship between economic growth and carbon emissions continue to…
We explore the potential multistability of the climate for a planet around the habitable zone. We focus on conditions reminiscent to those of the Earth system, but our investigation aims at presenting a general methodology for dealing with…
In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
Integrated Assessment Models (IAMs) of the climate and economy aim to analyze the impact and efficacy of policies that aim to control climate change, such as carbon taxes and subsidies. A major characteristic of IAMs is that their…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and…
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…
In order to better understand the occurrence of phase transitions, we adopt an approach based on the study of energy landscapes: The relation between stationary points of the potential energy landscape of a classical many-particle system…
In latitude-dependent energy balance models, ice-free and ice-covered conditions form physical boundaries of the system. With carbon dioxide treated as a bifurcation parameter, the resulting bifurcation diagram is nonsmooth with curves of…
Ecosystems tend to fluctuate around stable equilibria in response to internal dynamics and environmental factors. Occasionally, they enter an unstable tipping region and collapse into an alternative stable state. Our understanding of how…
Modern weather and climate models share a common heritage, and often even components, however they are used in different ways to answer fundamentally different questions. As such, attempts to emulate them using machine learning should…
Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…
The dryland vegetation model proposed by Rietkerk and collaborators has been explored from a bifurcation perspective in several previous studies. Our aim here is to explore in some detail the bifurcation phenomena present when the…
Despite major advances in climate science over the last 30 years, persistent uncertainties in projections of future climate change remain. Climate projections are produced with increasingly complex models which attempt to represent key…
A synergetic model describing the state of an ultrathin lubricant layer squeezed between two atomically smooth solid surfaces operating in the boundary friction mode has been developed further. To explain the presence of different operation…
Precipitation is one of the most important meteorological variables for defining the climate dynamics, but the spatial patterns of precipitation have not been fully investigated yet. The complex network theory, which provides a robust tool…
Social behaviour models are increasingly integrated into climate change studies, and the significance of climate tipping points for `runaway' climate change is well recognised. However, there has been insufficient focus on tipping points in…