相关论文: Fractal Stationary Density in Coupled Maps

We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…

We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and…

As a quantification of the main bottleneck to flow over a graph, the network property of conductance plays an important role in the process of synchronization of network-coupled dynamical systems. Diffusive coupling terms serve not only to…

This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…

Sensitivity to initial conditions is usually associated with chaotic dynamics and strange attractors. However, even systems with (quasi)periodic dynamics can exhibit it. In this context we report on the fractal properties of the isochrons…

We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically-coupled pendulums without any restrictions to their amplitudes (excluding a vicinity of $\pi$). Although this…

Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…

Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…

We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new…

Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis…

Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of…

This paper aims to review the measure synchronization, a weak form of synchronization observed in coupled Hamiltonian systems, briefly. This synchronization is characterized by a Hamiltonian system that displays either quasiperiodic or…

We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…

For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled…

This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…

Using dynamical density functional theory (DDFT) methods we investigate the laning instability of a sheared colloidal suspension. The nonequilibrium ordering at the laning transition is driven by non-affine particle motion arising from…

We study the stationary measures for variants of the Porous Medium Model in dimension 1. These are exclusion processes that belong to the class of kinetically constrained models, in which an exchange can occur between $x$ and $x+1$ only if…