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This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
Dynamic tolls present an opportunity for municipalities to eliminate congestion and fund infrastructure. Imposing tolls that regulate travel along a public highway through monetary fees raise worries of inequity. In this article, we…
The Vicsek-BGK equation is a kinetic model for alignment of particles moving with constant speed between stochastic reorientation events with sampling from a von Mises distribution. The spatially homogeneous model shows a steady state…
Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both the drift and volatility of the driving process. At a technical level, the analysis requires a…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some…
The definitions of temporal instability and of spatial instability in a flow system are comparatively surveyed. The simple model of one-dimensional Burgers' flow is taken as the scenario where such different conceptions of instability are…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…
We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…
We study a dynamic matching problem on a two-sided platform with unbalanced patience, in which long-lived supply accumulates over time with a unit waiting cost per period, while short-lived demand departs if not matched promptly. High- or…
Data-driven models (DDM) based on machine learning and other AI techniques play an important role in the perception of increasingly autonomous systems. Due to the merely implicit definition of their behavior mainly based on the data used…
The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When…
Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…