Abstract: This paper deals with some developments of the mathematical kinetic theory for active particles to model large systems of interacting entities whose microscopic state includes not only geometric and mechanical variables but also peculiar functions or specific activities. The analysis is specifically focused on modelling living open systems in view of optimization, control problems, and derivation of macroscopic equations from the underlying microscopic description. [Copyright &y& Elsevier]
Abstract: This paper deals with the qualitative analysis of a model describing the competition between tumor and immune cells. Such competition is characterized by proliferation–destruction phenomena and the interacting entities are characterized by a microscopic state which is modified by interactions. The model also includes the description of the natural trend of immune cells to reach a healthy or sentinel level, even when they have been involved in the competition with the tumor cells. The model is developed in the mathematical framework of the kinetic theory for active particles. [Copyright &y& Elsevier]
Abstract: This paper analyzes, on the basis of methods of the mathematical kinetic theory of active particles, some complexity problems related to the evolution of reciprocal feelings. Specifically, the analysis is focused on the complexity problems generated by triple interactions, with respect to simple binary encounters. Complexity refers not only to the structure of the equation, but also to the variable describing reciprocal feelings. [Copyright &y& Elsevier]