Predicting critical transitions in assortative spin-shifting networks.

Methods to forecast critical transitions, i.e. abrupt changes in systems' equilibrium states have relevance in scientific fields such as ecology, seismology, finance and medicine among others.

Early warning signals from the periphery: A model suggestion for the study of critical transitions.

Studies on the possibility of predicting critical transitions with statistical methods known as early warning signals (EWS) are often conducted on data generated with equation-based models (EBMs). These models base on difference or differential equations, which aggregate a system's components in a mathematical term and therefore do not allow for a detailed analysis of interactions on micro-level. As an alternative, we suggest a simple, but highly flexible agent-based model (ABM), which, when applying EWS-analysis, gives reason to (a) consider social interaction, in particular negative feedback effects, as an essential trigger of critical transitions, and (b) to differentiate social interactions, for example in network representations, into a core and a periphery of agents and focus attention on the periphery.

Training LSTM-neural networks on early warning signals of declining cooperation in simulated repeated public good games.

We present results of attempts to expand and enhance the predictive power of Early Warning Signals (EWS) for Critical Transitions (Scheffer et al. 2009) through the deployment of a Long-Short-Term-Memory (LSTM) Neural Network on agent-based simulations of a Repeated Public Good Game, which due to positive feedbacks on experience and social entrainment transits abruptly from majority cooperation to majority defection and back. Our method extension is inspired by several known deficiencies of EWS and by lacking possibilities to consider micro-level interaction in the so far primarily used simulation methods.

Hidden early-warning signals in scale-free networks.

Critical transitions of complex systems can often be predicted by so-called early-warning signals (EWS). In some cases, however, such signals cannot be detected although a critical transition is imminent. Observing a relation of EWS-detectability and the network topology in which the system is implemented, we simulate and investigate scale-free networks and identify which networks show, and which do not show EWS in the framework of a two state system that exhibits critical transitions.

Stable and transient multicluster oscillation death in nonlocally coupled networks.

In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multicluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations.

Chimera death: symmetry breaking in dynamical networks.

For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call "chimera death". We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling, two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations and a direct abrupt transition for larger coupling strength.