Related papers: Identifiability and Global Stability Analysis on S…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
In this paper, we study the probabilistic stability analysis of a subclass of stochastic hybrid systems, called the Planar Probabilistic Piecewise Constant Derivative Systems (Planar PPCD), where the continuous dynamics is deterministic,…
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…
Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
In this work, we present a scalable Linear Matrix Inequality (LMI) based framework to verify the stability of a set of linear Partial Differential Equations (PDEs) in one spatial dimension coupled with a set of Ordinary Differential…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. We deal with linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic equation…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
In the framework of the PDE's algebraic topology, previously introduced by A. Pr\'astaro, {\em exotic $n$-d'Alembert PDE's} are considered. These are $n$-d'Alembert PDE's, $(d'A)_n$, admitting Cauchy manifolds $N\subset (d'A)_n$…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Unlike ordinary differential equations (ODEs), linear partial differential equations (PDEs) admit multiple non-equivalent notions of stability. This variety makes interpretation of Lyapunov stability results challenging. \blue{To simplify…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…
We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system…