Related papers: Spatio-temporal representation of long-delayed sys…

This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential…

We propose a paradigmatic model system, a subcritical Hopf normal form subjected to noise and time-delayed feedback, to investigate the impact of time delay on coherence resonance in non-excitable systems. We develop analytical tools to…

Local causal states are latent representations that capture organized pattern and structure in complex spatiotemporal systems. We expand their functionality, framing them as spacetime autoencoders. Previously, they were only considered as…

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…

Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the…

Many decision making systems deployed in the real world are not static - a phenomenon known as model adaptation takes place over time. The need for transparency and interpretability of AI-based decision models is widely accepted and thus…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…

Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying observability requires knowledge of the equations governing the dynamics. These equations are often…

Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to…

Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs)…

It is shown that a general two-component feedback loop can be viewed as a deformed Hamiltonian system. Some of the implications of using ideas from theoretical physics to study biological processes are discussed.

This research addresses the problem of adaptive modeling in time-series data streams with clear input-output relationships. This problem is challenging because rapid system changes (regime shifts) caused by environmental factors or input…

We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…

We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…

Recent experiments have demonstrated the ability to manipulate nonlinear interactions via time modulation, giving rise to the so-called stroboscopic nonlinearity. To date, however, this phenomenon has not been subjected to a rigorous…

This paper is concerned with the study of continuous-time, non-smooth dynamical systems which arise in the context of time-varying non-convex optimization problems, as for example the feedback-based optimization of power systems. We…

Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…

Random delays weaken the temporal correspondence between actions and subsequent state feedback, making it difficult for agents to identify the true propagation process of action effects. In cross-task scenarios, changes in task objectives…