Related papers: Logistic map with memory from economic model
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
Discontinuities can be fairly arbitrary but also cause a significant impact on outcomes in larger systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression…
Lack of memory (locality in time) is a major limitation of almost all present time-dependent density functional approximations. By using semiclassical dynamics to compute correlation effects within a density-matrix functional approach, we…
We demonstrate the effectiveness of the logistic function to model the evolution of two economic systems. The first is the GDP and trade growth of the USA, and the second is the revenue and human resource growth of IBM. Our modelling is…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval {\Delta} results in…
Memories are stored, retained, and recollected through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions we construct a broad class of…
We empirically study the activity patterns of individual blog-posting and find significant memory effects. The memory coefficient first decays in a power law and then turns to an exponential form. Moreover, the inter-event time distribution…
We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is…
Memory, a fundamental component of human cognition, exhibits adaptive yet fallible characteristics as illustrated by Schacter's memory "sins".These cognitive phenomena have been studied extensively in psychology and neuroscience, but the…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…
This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying…
In this pedagogical study, carried out by adopting standard mathematical methods of nonlinear dynamics, we have presented some simple analytical models to understand terminal behaviour in industrial growth. This issue has also been…
Memory is a ubiquitous characteristic of complex systems and critical phenomena are one of the most intriguing phenomena in nature. Here, we propose an Ising model with memory and develop a corresponding theory of critical phenomena with…
This paper presents macroeconomic model that is based on parallels between macroeconomic multi-agent systems and multi-particle systems. We use risk ratings of economic agents as their coordinates on economic space. Aggregates of economic…
Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
Modal relaxation dynamics has been observed experimentally to clarify statistical-physical properties of soft-mode turbulence, the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals. We found a dual structure,…