Related papers: Delay Equations and Radiation Damping
Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects seems to be…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
The electron runaway phenomenon in plasmas depends sensitively on the momentum-space dynamics. However, efficient simulation of the global evolution of systems involving runaway electrons typically requires a reduced fluid description. This…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that they bare several problems. In…
The finite duration of collisions appear as time-nonlocality in the kinetic equation. Analyzing the corresponding quantum kinetic equation for dense interacting Fermi systems a delay differential equation is obtained which combines time…
The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased.…
Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset…
In this work we study local oscillations in delay differential equations with a frequency domain methodology. The main result is a bifurcation equation from which the existence and expressions of local periodic solutions can be determined.…
A system formed by a crowded environment of catalytic obstacles and complex oscillatory chemical reactions is inquired. The obstacles are static spheres of equal radius, which are placed in a random way. The chemical reactions are carried…
It is shown, that retardation in the $\alpha$-quenching in the Parker's dynamo model leads to parametric resonance. This result is observed in the numerical simulations and can be reproduced in the simple analytic model. The other…
In this paper we explore some surprising consequences of the retardation effects of Maxwell's electrodynamics to a system of charged particles. The specific cases of three interacting particles are considered in the framework of classical…
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
We consider a classical model of matter--radiation interaction, in which the matter is represented by a system of infinitely many dipoles on a one--dimensional lattice, and the system is dealt with in the so--called dipole (i.e. linearized)…
A simplified formula for light-deflection in the quadrupole field of moving massive bodies has been obtained in [1,2,3], which will be applied for Gaia data reduction. So far, in Gaia data reduction it has been assumed that the positions of…
An important question of ongoing interest for linear time-delay systems is to provide conditions on its parameters guaranteeing exponential stability of solutions. Recent works have explored spectral techniques to show that, for some…
The exact closed equation of motion for microscopic distribution function of classical many-body system with account of interactions retardation between particles is derived. It is shown that interactions retardation leads to irreversible…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…