Related papers: Aperiodic order via dynamical systems: Diffraction…
We show that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent.
It is shown how Adler's trace dynamics can be applied to stochastic mechanics and other complex classical dynamical systems. Emergent non-commutivity due to the fractal nature of sample trajectories is closely related to the fact that the…
The diffraction of a time-harmonic plane wave on collinear finite defects in a square lattice is studied. This problem is reduced to a matrix Wiener-Hopf equation. This work adapts the recently developed iterative Wiener-Hopf method to this…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order $s\in(1/2,1)$, singular nonlinearity, and gradient term under various situations, including nonlocal…
We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the smoothing properties of its solutions, which are shown to be…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
This paper is devoted to change-point detection using only the ordinal structure of a time series. A statistic based on the conditional entropy of ordinal patterns characterizing the local up and down in a time series is introduced and…
Periodic optical structures, such as diffraction grating and numerous photonic crystals, are one of the staples of modern nanophotonics for the manipulation of electromagnetic radiation. The array of subwavelength dielectric rods is one of…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…
We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.
In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for…