Related papers: Framework for global stability analysis of dynamic…
In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in…
We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are…
The stability of dynamical systems against perturbations (variations in initial conditions/model parameters) is a property referred to as structural stability. The study of sensitivity to perturbation is essential because in experiment…
Predictive safety filters enable the integration of potentially unsafe learning-based control approaches and humans into safety-critical systems. In addition to simple constraint satisfaction, many control problems involve additional…
Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world…
One of the fundamental concerns in the operation of modern power systems is the assessment of their frequency stability in case of inertia-reduction induced by the large share of power electronic interfaced resources. Within this context,…
During a financial crisis, the capital markets network frequently exhibits a high correlation between returns. We developed a network analysis framework based on daily returns from 42 countries to determine systemic stability. Our network…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
Multiple stable states - the coexistence of two or more distinct ecological configurations under identical environmental conditions - have attracted sustained interest in ecology, yet the field still lacks a unified framework connecting…
Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system's response, for example the speed of its recovery. We present a broadly applicable…
In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…
Research in multistable systems is a flourishing field with countless examples and applications across scientific disciplines. I present a catalog of multistable dynamical systems covering relevant fields of knowledge. This work is focused…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…
Active subspace analysis is a useful computational tool to identify and exploit the most important linear combinations in the space of a model's input parameters. These directions depend inherently on a quantity of interest, which can be…
Due to the evolving nature of power grids and model uncertainty, the online stability assessment of electrical power systems is always a challenging problem. This paper aims to provide a theoretical framework for estimating the region of…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Rising interest in the resilience of ecological systems has spawned diverse interpretations of the term's precise meaning. This paper classifies and explores definitions of resilience from the ecological literature using a dynamical systems…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…