Related papers: Generalized kinetic equations of dynamic system in…
The induced kinetic differential equation of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a polynomial differential equation, is it possible…
A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and…
Dynamic systems are ubiquitous in nature and are used to model many processes in biology, chemistry, physics, medicine, and engineering. In particular, systems of ordinary differential equations are commonly used for the mathematical…
The present work considers systems whose dynamics are governed by the nonlinear interactions among groups of 6 nonlinear waves, such as those described by the unforced quintic nonlinear Schr\"odinger equation. Specific parameter regimes in…
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is…
The thermodynamic approach to non-equilibrium dynamics describes the state of macroscopic systems by means of a collection of intensities or intensive variables. The latter are by definition the differentials of the entropy with respect to…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
We show a general kinetic equality for susceptibilities (KSE) of general fluctuating quantities and for the dynamical activity of nonequilibrium systems described by Markovian master equations. As special limiting cases, KSE reproduces the…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
A general method is discussed to obtain Markovian master equations which describe the interaction with the environment in a microscopic and non-perturbative fashion. It is based on combining time-dependent scattering theory with the concept…
Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the…
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
Kinematical and dynamical properties of chaotic systems are reviewed and a few applications are described.
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be…