Complex Systems: New Challenges with Modeling Headaches

This special issue follows, in this journal, various previous ones devoted to the contribution of mathematics to the modeling, qualitative analysis, and simulation of complex living systems, more precisely large systems constituted by several living entities interacting in a nonlinear manner. The focus of the previous issues was on specific topics such as biological systems and multi-particle systems, related to the ambitious aim of contributing to a mathematical theory of complex systems. This issue aims at contributing to the same objective by some speculations that link the contents to the mentioned challenging objective. A definition of complex systems, which is universally accepted by the scientific community, refers specifically to interactions and on their influence on collective emerging behaviors. The following definition can be quoted from Ref. 2: