Regions of multistability in some low-dimensional logistic models with excitation type coupling

TL;DR

This paper investigates the multistability regions in low-dimensional logistic models with excitation coupling, aiming to understand brain-like bistability phenomena through simplified network models.

Contribution

It identifies and reports the regions of bi- and multistability in coupled logistic map systems with excitation coupling, extending previous models to better mimic brain dynamics.

Findings

Regions of multistability are mapped and characterized.

Patterns of behavior are conserved across different network topologies.

The models mimic waking-sleeping bistability in brain systems.

Abstract

A naive model of many networked logistic maps with an excitation type coupling [Neural Networks, vol. 20, 102--108 (2007)], which is an extension of other low dimensional models, has been recently proposed to mimic the waking-sleeping bistability found in brain systems. Although the dynamics of large and complex aggregates of elementary components can not be understood nor extrapolated from the properties of a few components, some patterns of behavior could be conserved independently of the topology and of the number of coupled units. Following this insight, we have collected several of those systems where a few logistic maps are coupled under a similar mutual excitation scheme. The regions of bi- and multistability of these systems are sketched and reported.