Related papers: Deductive Stability Proofs for Ordinary Differenti…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
Boolean automata networks, genetic regulation networks, and metabolic networks are just a few examples of biological modelling by discrete dynamical systems (DDS). A major issue in modelling is the verification of the model against the…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay of network structures and the local dynamics of synchronous…
Eigenvalue perturbation theory is applied to justify using complex-valued linear scalar test equations to characterize the stability of implicit-explicit general linear methods (IMEX GLMs) solving autonomous linear ordinary differential…
This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability…
The interest of the scientific community for the existence, uniqueness and stability of solutions to PDE's is testified by the numerous works available in the literature. In particular, in some recent publications on the subject an…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of molecules where each molecule regulates its successor in a cycle.…
The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…
New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…
Structural stability is a necessary condition for successful construction of an assembly. However, designing a stable assembly requires a non-trivial effort since a slight variation in the design could significantly affect the structural…