Related papers: Internal noise interference to warnings of tipping…
Anticipating bifurcation-induced transitions in dynamical systems has gained relevance in various fields of the natural, social, and economic sciences. Before the annihilation of a system's equilibrium point by means of a bifurcation, the…
The phenomenon of critical slowing down (CSD) has played a key role in the search for reliable precursors of catastrophic regime shifts. This is caused by its presence in a generic class of bifurcating dynamical systems. Simple time-series…
Tipping points (TP) are often described as low-dimensional bifurcations, and are associated with early-warning signals (EWS) due to critical slowing down (CSD). CSD is an increase in amplitude and correlation of noise-induced fluctuations…
Regime shifts are quite common in complex systems like cell regulations, disease transmissions, ecosystems, marine ice instability, etc. Several statistical indicators known as early warning signals (EWS) have been theorized to anticipate…
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…
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…
The behavior of a dynamical system can exhibit abrupt changes when it crosses a tipping point. To prevent catastrophic events, it is useful to analyze indicators of the incoming bifurcation, as the divergence of the relaxation time of the…
Detection of critical slowing down (CSD) is the dominant avenue for anticipating critical transitions from noisy time-series data. Most commonly, changes in variance and lag-1 autocorrelation [AC(1)] are used as CSD indicators. However,…
In this work, we analyse the effect of adding Gaussian white noise to the slow variable of a slow--fast system passing through a saddle--node (or fold) bifurcation. This problem is mainly motivated by applications to non-equilibrium energy…
Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…
Many dynamical systems, including power systems, recover from perturbations more slowly as they approach critical transitions---a phenomenon known as critical slowing down. If the system is stochastically forced, autocorrelation and…
Warning signs for tipping points (or critical transitions) have been very actively studied. Although the theory has been applied successfully in models and in experiments for many complex systems such as for tipping in climate systems,…
Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can…
In a nonautonomous nonlinear dynamical system, generic critical transitions (tipping points) are not limited to slow passage through fold bifurcations. They can also correspond to slow passage through other generic bifurcations, such as…
Many natural and man-made systems are prone to critical transitions -- abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal (EWS) for critical transitions by learning generic…
Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress…
Statistical early warning signs can be used to identify an approaching bifurcation in stochastic dynamical systems and are now regularly employed in applications concerned with the identification of potential rapid, non-linear change or…
Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points when control parameters are varied…
We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations,…
We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…