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We investigate a low-dimensional slow-fast model to understand the dynamical origin of El Ni\~no-Southern Oscillation. A close inspection of the system dynamics using several bifurcation plots reveals that a sudden large expansion of the…
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…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
Dansgaard-Oeschger events are a prominent mode of variability in the records of the last glacial cycle. Various prototype models have been proposed to explain these rapid climate fluctuations, and no agreement has emerged on which may be…
Transitions between distinct dynamical regimes are ubiquitous in nonequilibrium systems. As a prototypical example, deposition growth is often accompanied by irreversible morphological instabilities. Forecasting such transitions from…
Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced…
It is well known that the addition of noise in a multistable system can induce random transitions between stable states. The rate of transition can be characterised in terms of the noise-free system's dynamics and the added noise: for…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
Phase transitions are emergent phenomena where microscopic interactions drive a disordered system into a collectively ordered phase. Near the boundary between two phases, the system can exhibit critical, scale-invariant behavior. Here, we…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state.…
Developing methods for detecting tipping phenomena at an early stage is an important problem in various fields such as ecology, medicine, and economics. A tipping phenomenon is characterized by a rapid transition resulting from the…
We study a two-dimensional low-dissipation dynamical system with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system…
We present a phenomenological description of the critical slowing down associated with period-doubling bifurcations in discrete dynamical systems. Starting from a local Taylor expansion around the fixed point and the bifurcation parameter,…
The high-frequency band of the $\delta^{18}\mbox{O}$ variations in the North Greenland Ice Core Project displays fluctuation levels that increase as one approaches the onset of an interstadial (warm) period. For some of the events it is…
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…
Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…
We report on self-induced switchings between multiple distinct space--time patterns in the dynamics of a spatially extended excitable system. These switchings between low-amplitude oscillations, nonlinear waves, and extreme events strongly…
This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable…
Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate…