Related papers: Relaxation oscillations in an idealized ocean circ…
The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the…
We discuss the relaxation dynamics of a simple lattice gas model for glass-forming systems and show that with increasing density of particles this dynamics slows down very quickly. By monitoring the trajectory of tagged particles we find…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here we introduce a new model for…
The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points…
We consider planar systems of predator-prey models with small predator death rate $\epsilon>0$. Using geometric singular perturbation theory and Floquet theory, we derive characteristic functions that determines the location and the…
We study the dynamics of a circadian oscillator model which was proposed by Tyson, Hong, Thron and Novak. This model indicates a molecular mechanism for the circadian rhythm in Drosophila. After giving a detailed study of the equilibria, we…
Simple conditions have been developed in [Zhang, Wahl and Yu, SIAM Rev. 2014; Yu and Wang, Math. Biosci. Eng. 2019], which are used to identify the existence of slow-fast relaxation oscillations that appear in differential systems, where…
The Atlantic Meridional Overturning Circulation (AMOC) is a key component of the Earth's climate. Evidence indicates a twentieth-century weakening, and enhanced freshwater input to the subpolar North Atlantic may further reduce overturning…
Annealing schedule control provides new opportunities to better understand the manner and mechanisms by which putative quantum annealers operate. By appropriately modifying the annealing schedule to include a pause (keeping the Hamiltonian…
We introduce a new simple hierarchically constrained model of slow relaxation. The configurational energy has a simple form as there is no coupling among the spins defining the system; the associated stationary distribution is an…
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of parameters, the corresponding system of ordinary…
Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his eponymous paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced…
Metriplectic dynamical systems consist of a special combination of a Hamiltonian and a (generalized) entropy-gradient flow, such that the Hamiltonian is conserved and entropy is dissipated/produced (depending on a sign convention). It is…
In this study, we formulate a set of differential equations for a binary system to describe the secular-tidal evolution of orbital elements, rotational dynamics, and deformation (flattening), under the assumption that one body remains…
Transition to thermal equilibrium in a uniformly heated two-dimensional harmonic triangular lattice with nearest neighbor interactions is investigated. Initial conditions, typical for molecular dynamics simulations, are considered.…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…
We study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to a system of two harmonic oscillators for some characteristic time interval. We show that, for the case where the…
We review the results obtained in [GMPV] and [GV] on the stochastic and statistical stability of the classical Lorenz flow, where, looking at the Lorenz'63 ODE system as a simple - yet non trivial - model of the atmospheric circulation, the…
We consider the asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. We analytically obtain the exact time evolution of correlation functions with arbitrary length starting from the initial state with no…