This review paper is devoted to study the conceptual difficulties that mathematics meets
when attempting to describe the complexity of living matter focusing on the challenging …

The modeling of living systems composed of many interacting entities is treated in this paper
with the aim of describing their collective behaviors. The mathematical approach is …

This paper presents a unified mathematical theory of swarms where the dynamics of social
behaviors interacts with the mechanical dynamics of self-propelled particles. The term …

In this paper, we present a survey of recent progress on the emergent behaviors of
stochastic particle models which arise from the modeling of collective dynamics. Collective …

The Nobel Prize in Physics 2021 was awarded “for groundbreaking contributions to our
understanding of complex systems” according to the prize committee. Half of the prize …

This paper proposes a further development of the mathematical theory of swarms to
behavioral dynamics of social and economic systems, with an application to the modeling of …

The aim of this Element is to understand how far mathematical theories based on active
particle methods have been applied to describe the dynamics of complex systems in …

In the present paper, we study a diauxic growth that can be generated by a class of model at
the mesoscopic scale. Although the diauxic growth can be related to the macroscopic scale …

This editorial paper presents a special issue devoted to the development of mathematical
tools from kinetic and swarms theory to the modeling and simulations of the dynamics of …

Celem rozprawy jest dokonanie matematycznego opisu cyklu komórkowego,
uwzględniającego wpływ różnych białek na regulację czasu rozpoczęcia podziału komórki …