Complex Fuzzy Systems and Their Collective Behavior

This work aims at being a contribution for the characterization of a new class of complex systems built as arrays of coupled fuzzy logic based chaotic oscillators and an investigation on their collective dynamical features. Different experiments were carried out varying the parameters related to the single-unit dynamics, as Lyapunov exponent, and to the macrosystem structure, as the number of connections. Four types of global behaviors have been identified and characterized distinguishing their patterns as follows: the spatiotemporal chaos, the regular synchronized behavior, the transition phase, and the chaotic synchronized behavior. These collective behaviors and the synchronization capability have been highlighted by defining a mathematical indicator which weights the slight difference among a wide number of spatiotemporal patterns. To investigate the effects due to the network architecture on the synchronization characteristics, complex fuzzy systems have been reproduced using fuzzy chaotic cells connected through different topologies: regular, “small worlds,” and random.