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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…
One of the most common hypotheses on the theory of non-smooth dynamical systems is a regular surface as switching manifold, at which case there is at least well-defined and established Filippov dynamics. However, systems with singular…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
The friction force, friction coefficients and the effects on the dynamics of particles, bodies and systems, are fundamental themes in university physics of the first cycles and also in general physics courses of upper secondary education in…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the…
The stability of dynamical systems against perturbations (variations in initial conditions/model parameters) is a property referred to as structural stability. The study of sensitivity to perturbation is essential because in experiment…
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role…
In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
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…
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…
The results of investigations of main characteristics of a one-dimensional percolation theory (percolation threshold, critical exponents of correlation radius and specific heat, and free energy) are presented for the problem of bonds and…
Hysteresis can be defined from a dynamical systems perspective with respect to equilibrium points. Consequently, hysteresis naturally lends itself as a topic to illustrate and extend concepts in a dynamical systems course. A number of…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…