Abstract
This paper is motivated by the perspective ideas proposed in our previous studies, where some challenging problems, for instance qualitative analysis of the solution to nonlinear problems and micro-macro asymptotic analysis, where posed. Our work focuses on the study of the interactions between learning dynamics and other types of dynamics which can be modeled by kinetic theory methods. The contents are presented in three parts. First, a general description of different theories of learning dynamics within the framework of cognitive sciences is critically analyzed with the aim of capturing the main features of the system towards modeling. Subsequently, the class of systems which are the object of the modeling approach is defined by showing how the previous structure can be developed, thanks to new conceptual ideas, including the concept of symmetric and asymmetric learning, towards modeling. Finally, some applications are selected to show how the approach can be methodologically applied.
Highlights
This paper is motivated by the perspective ideas proposed in our previous studies, where some challenging problems, for instance qualitative analysis of the solution to nonlinear problems and micro-macro asymptotic analysis, where posed
This present paper focuses on the study of the interactions between learning dynamics and other types of dynamics that can be accounted for by kinetic theory tools
Connected with the previous analysis is the concept of collective learning which is a complex dynamics that has been variously defined in different ways
Summary
A mathematical approach to the collective learning dynamics has been developed in [1,2,3] to model individual and collective learning by interactions involving individuals and groups of individuals. The contents of our paper rely on the observation that the perspective ideas proposed in [1] leave open various problems that are definitely worth of future investigations In more detail, this present paper focuses on the study of the interactions between learning dynamics and other types of dynamics that can be accounted for by kinetic theory tools. These applications refer to the two aforementioned dynamics, firstly the modeling of wealth policy opposition to governments up to radicalization and the interaction between learning walking strategy in crowd dynamics. The presentation of these case studies concludes with a critical analysis that, starting from the theoretical achievements of our paper, looks ahead to research perspectives
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