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A naive model of many networked logistic maps with an excitation typecoupling [Neural Networks, vol. 20, 102--108 (2007)], which is an extension ofother low dimensional models, has been recently proposed to mimic thewaking-sleeping bistability found in brain systems. Although the dynamics oflarge and complex aggregates of elementary components can not be understood norextrapolated from the properties of a few components, some patterns of behaviorcould be conserved independently of the topology and of the number of coupledunits. Following this insight, we have collected several of those systems wherea few logistic maps are coupled under a similar mutual excitation scheme. Theregions of bi- and multistability of these systems are sketched and reported.

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