Related papers: A dynamically-consistent nonstandard finite differ…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant $\delta$-scrambled set for some $\delta>0$ if…
In this work, we consider a class of dynamical systems described by ordinary differential equations under the assumption that the global asymptotic stability (GAS) of equilibrium points is established based on the Lyapunov stability theory…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
An actively controlled Susceptible-Infected-Susceptible (actSIS) contagion model is presented for studying epidemic dynamics with continuous-time feedback control of infection rates. Our work is inspired by the observation that epidemics…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback…
In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…
We consider a susceptible-infected-susceptible (SIS) epidemic model in which a large group of individuals decide whether to adopt partially effective protection without being aware of their individual infection status. Each individual…
In this paper we discuss a new discretization for the Biot equations. The discretization treats the coupled system of deformation and flow directly, as opposed to combining discretizations for the two separate sub-problems. The coupled…
This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We…
We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
Based on the classical continuous system initially proposed by Bailey in 1975, we present a novel Susceptible--Infected--Removed (SIR) model defined in quantum time, where the temporal evolution is governed by a non-uniform time grid. An…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with…