Related papers: The One-dimensional Version of Peixoto's Structura…

We derive discrete and continuous class of mathematical models that describe a progressive collapse in a fictional one-dimensional structure, where we consider plastic and elastic types of collisions. We examine static (collapse initiation…

The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…

We present a streamlined account of recent developments in the stability theory for planar viscous shock waves, with an emphasis on applications to physical models with ``real,'' or partial viscosity. The main result is the establishment of…

This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…

This paper investigates the stability properties of discrete-time multilinear dynamical systems via tensor spectral theory. In particular, if the dynamic tensor of a multilinear dynamical system is orthogonally decomposable (odeco), we can…

Verification of discrete time or continuous time dynamical systems over the reals is known to be undecidable. It is however known that undecidability does not hold for various classes of systems: if robustness is defined as the fact that…

Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

The dynamics of the discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is investigated by Monte Carlo simulations. The mobility of the growing surface was studied as a function of a small driving force…

In this paper, the stability of longitudinal vibrations for transmission problems of two smart-system designs are studied: (i) a serially-connected Elastic-Piezoelectric-Elastic design with a local damping acting only on the piezoelectric…

We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…

This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

This paper proposes a unified approach for dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a non-minimal description in terms of…

In a series of papers, Avalos and Triggiani established the fluid-elastic semigroup for the coupled Stokes-Lam\'e system modelling the coupled dynamics of a linearly elastic structure immersed in a viscous Newtonian fluid. They analyzed the…

We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…

A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…

We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…

Mathematical models of glucose, insulin, and pancreatic $\beta$-cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the Topp model's discrete-time dynamics to represent…

This article is dedicated to the study of diagonal hyperbolic systems in one space dimension, with cumulative distribution functions, or more generally nonconstant monotonic bounded functions, as initial data. Under a uniform strict…