Bistability: a common feature in some "aggregates" of logistic maps

Abstract

As it was argued by Anderson [Science 177, 393 (1972)], the "reductionist" hypothesis does not by any means imply a "constructionist" one. Hence, in general, the behavior of large and complex aggregates of elementary components can not be understood nor extrapolated from the properties of a few components. Following this insight, we have simulated different "aggregates" of logistic maps according to a particular coupling scheme. All these aggregates show a similar pattern of dynamical properties, concretely a bistable behavior, that is also found in a network of many units of the same type, independently of the number of components and of the interconnection topology. A qualitative relationship with brain-like systems is suggested.