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Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…

Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…

In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…

We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…

As attribution-based explanation methods are increasingly used to establish model trustworthiness in high-stakes situations, it is critical to ensure that these explanations are stable, e.g., robust to infinitesimal perturbations to an…

We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…

This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a…

We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced…

The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…

We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…

We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary,…

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…

Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…

The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…