Introduction to Double Focus Issue: Nonautonomous dynamical systems in the sciences

This Double Focus Issue consists of two linked Focus Issues—(a) Nonautonomous dynamical systems: Theory, methods, and applications and (b) Nonautonomous dynamics in the climate sciences, which we refer to as NDS-G and NDS-C, for short, where “G” stands for general and “C” for climate. Nonlinear dynamics has achieved a leading status in the mathematical, physical, and life sciences over the last couple of decades. A very significant recent direction is dealing with the role of time dependence in the external forcing and the parameters of the models under study. Paramount examples concern the role of anthropogenic effects on climate and biodiversity or of ageing on biomedical problems. The mathematical theory of such effects is developing rapidly via the study of NDSs and random dynamical systems. Applications are blossoming and have in return been driving further developments of the theory. These theoretical advances and their application to an increasing number of areas of the physical, life, and socioeconomic sciences were on view in two recent meetings: a three-day minisymposium within the framework of Dynamics Days Europe 2023 in Naples, Italy, and an International Seminar and Workshop in Dresden, Germany, in October 2023. Discussions at these two events led to this Double Focus Issue, taking contributions from a wide community of researchers in the relevant areas.