For studying biological conditions with higher precision, the memory characteristics defined by the fractional-order versions of living dynamical systems have been pointed out as a meaningful approach. Therefore, we analyze the dynamics of a glucose-insulin regulatory system by applying a non-local fractional operator in order to represent the memory of the underlying system, and whose state-variables define the population densities of insulin, glucose, and $\beta$-cells, respectively. We focus mainly on four parameters that are associated with different disorders (type 1 and type 2 diabetes mellitus, hypoglycemia, and hyperinsulinemia) to determine their observation ranges as a relation to the fractional-order. Like many preceding works in biosystems, the resulting analysis showed chaotic behaviors related to the fractional-order and system parameters. Subsequently, we propose an active control scheme for forcing the chaotic regime (an illness) to follow a periodic oscillatory state, i.e., a disorder-free equilibrium. Finally, we also present the electronic realization of the fractional glucose-insulin regulatory model to prove the conceptual findings.

In this work, a synchronization scheme for networks of complex systems is presented. The proposed synchronization scheme uses a control law obtained with some definitions from graph theory and solving the Model-Matching Problem for complex networks. In particular, Rössler, Chen, Lorenz and Lü chaotic systems are used as complex chaotic systems into complex networks. Particular cases with regular and irregular networks of six identical chaotic systems are implemented, with some well-known topologies as star and ring small-world, and tree topologies. Highlighting, the obtained control law is applied to synchronize an irregular network of six different chaotic systems in a tree topology. The usefulness and advantages of the proposed synchronization scheme are highlighted performing numerical simulations of the chaotic complex networks.