The proposed goal is to study asymptotic behaviors (stability, dichotomy, trichotomy, splitting) for dynamical systems described by evolution equations, equations with differences both if the state space is finite in size and in the case of Banach spaces. A qualitative study is envisaged in which uniform, non-uniform behaviors in relation to different growth and decrease rates are highlighted. Applications of Mathematical Analysis in optimization, differential equations and in various related fields with interdisciplinary impact will be highlighted. The topic also includes the study of bifurcation systems using classical whole-order derivatives, as well as fractional derivatives, but also applications in economics and biology that address the processes from several points of view: deterministic, stochastic and uncertain taking into account delays that may to show up.
The project is based on the results obtained by the team so far, reflected in the publications in prestigious international journals, as well as the citations of these results by internationally recognized mathematicians.