Related papers: The stability index for dynamically defined Weiers…
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static…
Multiple analytical and empirical stability criteria have been derived in the literature for two planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well…
We propose the application of occupation measure theory to the classical problem of transient stability analysis for power systems. This enables the computation of certified inner and outer approximations for the region of attraction of a…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…
The classical (inviscid) stability analysis of shock waves is based on the Lopatinski determinant, \Delta---a function of frequencies whose zeros determine the stability of the underlying shock. A careful analysis of \Delta\ shows that in…
In this paper we study the stability and deformation of structures, in particular the wall of an open pit mine is studied by using information obtained from a variety of remote sensors and some extra data, with a novelty approach…
We study by a combination of numerical and analytical Evans function techniques the stability of solitary wave solutions of the St. Venant equations for viscous shallow-water flow down an incline, and related models. Our main result is to…
We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions in…
We study the dynamical behavior of a one dimensional interface interacting with a sticky unpenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contact between the interface and the substrate…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
The small-signal stability of multi-terminal HVDC systems, which is related to the dynamic interactions among different VSCs through the coupling of DC and AC networks, has become one of the important issues for the safety and stable…
This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of…
We consider periodic solutions to equations of Korteweg-Devries type. While the stability theory for periodic waves has received much some attention the theory is much less developed than the analogous theory for solitary wave stability,…
The global stability of the nonhomogeneous positive steady state solution to a diffusive Holling-Tanner predator-prey model in a heterogeneous environment is proved by using a newly constructed Lyapunov function and estimates of nonconstant…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define…