Related papers: Variations in stability revealed by temporal asymm…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
In financial markets, greater volatility is usually considered synonym of greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
Prior research has shown that autocorrelation and variance in voltage measurements tend to increase as power systems approach instability. This paper seeks to identify the conditions under which these statistical indicators provide reliable…
The stability of a complex system generally decreases with increasing system size and interconnectivity, a counterintuitive result of widespread importance across the physical, life, and social sciences. Despite recent interest in the…
Norms of Persistent Homology introduced in topological data analysis are seen as indicators of system instability, analogous to the changing predictability that is captured in financial market uncertainty indexes. This paper demonstrates…
Linear stability analysis is applied to the mean flow of an oscillating round jet with the aim to investigate the robustness and accuracy of mean flow stability wave models. The jet's axisymmetric mode is excited at the nozzle lip through a…
We propose a novel framework for modeling time-varying persistence in economic time series, allowing for smoothly evolving heterogeneity in shock dynamics. We leverage localized regression techniques to flexibly identify changes in…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
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…
Unsteadiness lies at the heart of turbulent fluid dynamics, eddy formation and instabilities in flows thus making it central to both understanding and controlling fluid systems. In this work, we present an objective measure for the…
Many parts of the Earth system are thought to have multiple stable equilibrium states, with the potential for rapid and sometimes catastrophic shifts between them. The most common frameworks for analyzing stability changes, however, require…
We consider stochastic electro-mechanical dynamics of an overdamped power system in the vicinity of the saddle-node bifurcation associated with the loss of global stability such as voltage collapse or phase angle instability. Fluctuations…
The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we analyze the stability of a system under distribution…
One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known…
This article concerns the stability of a model for mass-spring systems with positive damping and negative stiness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the…
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…
The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…