Related papers: Long-term memory contribution as applied to the mo…

We report short-term memory formation in a nonlinear dynamical system with many degrees of freedom. The system ``remembers'' a sequence of impulses for a transient period, but it coarsens and eventually ``forgets'' nearly all of them. The…

Many natural and social systems possess power-law memory, and their mathematical modeling requires the application of discrete and continuous fractional calculus. Most of these systems are nonlinear and demonstrate regular and chaotic…

The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional order damping. For that purpose, we use the Grunwald-Letnikov fractional derivative…

We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of memory loss. The maps may be chosen in any…

This paper introduces a special type of systems, defines their properties, and then demonstrates that a reduction machine for pure untyped extensional lambda calculus can be implemented as a system of the introduced type. Specifically, we…

We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result…

Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…

A stochastic model, the product of a circulant matrix and a random normal vector, is shown to produce an evolutive long memory time series with a power law spectral density. The distribution of the time series, a beta location scale family…

Conventional wisdom indicates that initial memory should decay away exponentially in time for general (noncritial) equilibration processes. In particular, time-integrated quantities such as heat are presumed to lose initial memory in a…

In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.

Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an…

Dynamics of the imbalance in occupations on even and odd sites of a lattice serves as one of the key characteristics for identification of the many-body localization transition. In this work, we investigate the long-time behaviour of the…

We study the generalized dynamic factor model in a long-memory setting. Unlike most recent work, which assumes a finite-dimensional factor space and short memory, our framework allows the factor space to be infinite-dimensional and the…

A systematic investigation of the effect of the history force on particle advection is carried out for both heavy and light particles. General relations are given to identify parameter regions where the history force is expected to be…

We explore different families of quasi-periodically Forced Logistic Maps for the existence of universality and self-similarity properties. In the bifurcation diagram of the Logistic Map it is well known that there exist parameter values…

Disordered and amorphous materials often retain memories of perturbations they have experienced since preparation. Studying such memories is a gateway to understanding this challenging class of systems, yet it often requires the ability to…

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…

When involution affects individuals, their efforts do not augment resources but merely compete for limited resources. From entrance exams to company overtime, such efforts lead to unnecessary costs, undermining group welfare. Meanwhile, the…

The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and…

Reliable traffic flow prediction is crucial to creating intelligent transportation systems. Many big-data-based prediction approaches have been developed but they do not reflect complicated dynamic interactions between roads considering…