Related papers: Timing of Transients: Quantifying Reaching Times a…
How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest, and has stimulated a lot of activities in dynamical and stochastic systems…
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,…
Many real-world systems undergo abrupt changes in dynamics as they move across critical points, often with dramatic consequences. Much existing theory on identifying the time-series signatures of nearby critical points -- such as increased…
The problem of quickest change detection (QCD) under transient dynamics is studied, where the change from the initial distribution to the final persistent distribution does not happen instantaneously, but after a series of transient phases.…
Previous studies have shown that rate-induced transitions can occur in pullback attractors of systems subject to "parameter shifts" between two asymptotically steady values of a system parameter. For cases where the attractors limit to…
Estimating uncertainty for AI agents in real-world multi-turn tool-using interaction with humans is difficult because failures are often triggered by sparse critical episodes (e.g., looping, incoherent tool use, or user-agent…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
Criticality metrics such as time-to-collision (TTC) quantify collision urgency but conflate the consequences of false-positive (FP) and false-negative (FN) perception errors. We propose two novel effort-based metrics: False Speed Reduction…
In this paper, the tracking control problem of an Euler-Lagrange system is addressed with regard to parametric uncertainties, and an adaptive-robust control strategy, christened Time-Delayed Adaptive Robust Control (TARC), is presented.…
Rate-induced tipping (R-tipping) occurs when time-variation of input parameters of a dynamical system interacts with system timescales to give genuine nonautonomous instabilities. Such instabilities appear as the input varies at some…
Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
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…
In this paper, the tracking control problem of a class of Euler-Lagrange systems subjected to unknown uncertainties is addressed and an adaptive-robust control strategy, christened as Time-Delayed Adaptive Robust Control (TARC) is…
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
The limiting temporal resolution of a time-domain survey in detecting transient behavior is set by the time between observations of the same sky area. We analyze the distribution of visit separations for a range of Vera C. Rubin Observatory…
We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…
New time-domain surveys, such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), will observe millions of transient alerts each night, making standard approaches of visually identifying new and interesting transients…
Recurrence time quantifies the duration required for a physical system to return to its initial state, playing a pivotal role in understanding the predictability of complex systems. In quantum systems with subspace measurements, recurrence…