A simple scalar coupled map lattice model for excitable media

A simple scalar coupled map lattice model for excitable media is intensively analysed in this paper. This model is used to explain the excitability of excitable media, and a Hopf-like bifurcation is employed to study the different spatio-temporal patterns produced by the model. Several basic rules for the construction of these kinds of models are proposed. Illustrative examples demonstrate that the sCML model is capable of generating complex spatiotemporal patterns

Risk Control for Synchronizing a New Economic Model

Risk analysis in control problems is a critical but often overlooked issue in this research area. The main goal of this analysis is to assess the reliability of designed controllers and their impact on applied systems. The chaotic behavior of fractional-order economical systems has been extensively investigated in previous studies, leading to advancements in such systems. However, this chaotic behavior poses unpredictable risks to the economic system. This paper specifically investigates the reliability and risk analysis of chaotic fractional-order systems synchronization. Furthermore, we present a technique as a new mechanism to evaluate controller performance in the presence of obvious effects. Through a series of simulation studies, the reliability and risk associated with the proposed controllers are illustrated. Ultimately, we show that the suggested technique effectively reduces the risks associated with designed controllers

Numerical solution of the stochastic neural field equation with applications to working memory

The main goal of the present work is to investigate the effect of noise in some neural fields, used to simulate working memory processes. The underlying mathematical model is a stochastic integro-differential equation. In order to approximate this equation we apply a numerical scheme which uses the Galerkin method for the space discretization. In this way we obtain a system of stochastic differential equations, which are then approximated in two different ways, using the Euler–Maruyama and the Itô–Taylor methods. We apply this numerical scheme to explain how a population of cortical neurons may encode in its firing pattern simultaneously the nature and time of sequential stimulus events. Numerical examples are presented and their results are discussed.The authors acknowledge the financial support of the Portuguese FCT (Fundacao para a Ciencia e Tecnologia), Portugal, through projects UIDB/04621/2020, UIDP/04621/2020 (IST), UIDB/00013/2020, UIDP/00013/2020 (UMinho) and PTDC/MAT-APL/31393/2017. The authors are also grateful to the reviewers for their careful reading of the text and helpful suggestions that contributed to the improvement of the article