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We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The microscopic deterministic mechanism of the irreversible equilibration process in…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the…
In this paper, we delve into the study of the generalized KP equation, which incorporates double-power nonlinearities. Our investigation covers various aspects, including the existence of solitary waves, their nonlinear stability, and…
We study the stability of unitary quantum dynamics of composite systems (for example: central system + environment) with respect to weak interaction between the two parts. Unified theoretical formalism is applied to study different physical…
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
The dynamics of the solutions to a class of conservative SPDEs are analysed from two perspectives: Firstly, a probabilistic construction of a corresponding random dynamical system is given for the first time. Secondly, the existence and…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
We study the well-posedness and stability of an impedance passive infinite-dimensional linear system under nonlinear feedback of the form $u(t)=\phi(v(t)-y(t))$, where $\phi$ is a monotone function. Our first main result introduces…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
In this paper a fairly complete mathematical model of CP-PLL, which reliable enough to serve as a tool for credible analysis of dynamical properties of these circuits, is studied. We refine relevant mathematical definitions of the hold-in…
The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is…
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…
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…
Particles confined in droplets are called compound particles. They are encountered in various biological and soft matter systems. Hydrodynamics can play a decisive role in determining the configuration and stability of these multiphase…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
In this paper we discuss the application of the harmonic balance method for the global analysis of the classical phase-locked loop (PLL) circuit. The harmonic balance is non rigorous method, which is widely used %,often without rigorous…