We consider a set of mobile agents in a two dimensional space, each one of them carrying a chaotic oscillator, and discuss the related synchronization issues under the framework of time-variant networks. In particular, we show that, as far as the time scale for the motion of the agents is much shorter than that of the associated dynamical systems, the global behavior can be characterized by a scaled all-to-all Laplacian matrix, and the synchronization conditions depend on the agent density on the plane.

Chaos and random signals share the property of long term unpredictable irregular behavior and broad band spectrum. The aim of this paper is not to distinguish between random and chaotic dynamics, nor to show the use of chaos, but to focus attention on how chaos and noise help order to arise from disorder It means to investigate the effect of the introduction of either deterministic chaotic or random sequences in different types of phenomena. In particular the results related to different applications, self-organization in arrays of locally coupled systems in which a chaotic dissymmetry is present, chaos driven optimization strategies, pattern formation in Drosophila embryos and some new topics on game theory are treated with the aim to investigate the subject: "does chaos work better than noise?".

In this work we study the effect of behavioral changes of individuals on the propagation of epidemic diseases. Specifically, we consider a susceptible-infected-susceptible model over a network of contacts that evolves in a time scale that is comparable to the individual disease dynamics. The phenomenon is modeled in the context of activity-driven networks, in which contacts occur on the basis of activity potentials. To offer insight into behavioral strategies targeting both susceptible and infected individuals, we consider two separate behaviors that may emerge in respiratory syndromes and sexually transmitted infections. The first is related to a reduction in the activity of infected individuals due to quarantine or illness. The second is instead associated with a selfish self-protective behavior of susceptible individuals, who tend to reduce contact with the rest of the population on the basis of a risk perception. Numerical and theoretical results suggest that behavioral changes could have a beneficial effect on the disease spreading, by increasing the epidemic threshold and decreasing the steady-state fraction of infected individuals.