Coexisting Attractors and Complex Basins in Discrete-time Economic Models

Author(s):  
Gian Italo Bischi ◽  
Fabio Lamantia
2009 ◽  
Vol 19 (10) ◽  
pp. 3283-3309 ◽  
Author(s):  
ALFREDO MEDIO ◽  
MARINA PIREDDU ◽  
FABIO ZANOLIN

This article describes a method — called here "the method of Stretching Along the Paths" (SAP) — to prove the existence of chaotic sets in discrete-time dynamical systems. The method of SAP, although mathematically rigorous, is based on some elementary geometrical considerations and is relatively easy to apply to models arising in applications. The paper provides a description of the basic mathematical ideas behind the method, as well as three applications to economic models. Incidentally, the paper also discusses some questions concerning the definition of chaos and some problems arising from economic models in which the dynamics are defined only implicitly.


1994 ◽  
Vol 213 (3) ◽  
Author(s):  
Herman J. Nieuwenhuis ◽  
Lambert Schoonbeek

SummaryWe compare the dynamic behaviour of a given linear economic model with continuous time and two discrete time models derived from it. The latter two models with discrete time play an important role in the literature on econometric models with continuous time. We analyze and compare the eigenvalues of the models, and obtain results with respect to the stability behaviour and the periods of oscillations that arise in the case of complex eigenvalues.


2021 ◽  
Vol 5 (4) ◽  
pp. 202
Author(s):  
A. Othman Almatroud

At present, the extreme multistability of fractional order neural networks are gaining much interest from researchers. In this paper, by utilizing the fractional ℑ-Caputo operator, a simple fractional order discrete-time neural network with three neurons is introduced. The dynamic of this model are experimentally investigated via the maximum Lyapunov exponent, phase portraits, and bifurcation diagrams. Numerical simulation demonstrates that the new network has various types of coexisting attractors. Moreover, it is of note that the interesting phenomena of extreme multistability is discovered, i.e., the coexistence of symmetric multiple attractors.


Methodology ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 41-60
Author(s):  
Shahab Jolani ◽  
Maryam Safarkhani

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.


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