Dynamics on Discrete Systems

Discrete systems like networks, simplicial complexes or metaplexes exist for the transmission of effects between their integrand parts. Therefore, the dynamical processes play fundamental role in understanding the functioning of complex systems. I am interested in the mathematical analysis and applications of several kinds of dynamics of these systems. In particular I am focusing on: (i) Normal and anomalous diffusive processes on networks, hypernetworks, simplicial complexes and metaplexes; (ii) The analytical study of compartment epidemiological models like Susceptible-Infected, and Susceptible-Infected-Susceptible, for the analysis of risk in complex systems and the transmission of effects in biological systems; (iii) Generalized synchronization processes with the use of the different kinds of Laplacian operators developed in other areas of my research; (iv) Use of fractional calculus for generalizing dynamical processes on graphs and networks.