Abstract
This paper deals with the modelling of complex sociopsychological games and reciprocal feelings involving interacting individuals. The modelling is based on suitable developments of the methods of mathematical kinetic theory of active particles with special attention to modelling multiple interactions. A first approach to complexity analysis is proposed referring to both computational and modelling aspects.
Highlights
This paper deals with the modelling of complex sociopsychological games and reciprocal feelings based on some conceptual developments of a new class of kinetic equations recently proposed in the literature to model the evolution of large systems of interacting individuals such that their microscopic state is defined by mechanical variables, and by additional variables, describing social and/or biological functions or behaviors
The guiding lines of the above mathematical approach is the derivation of an evolution equation for the statistical distribution over the microscopic state, which, as a particular case, may be related to a somehow intelligent, or at least organized, behavior of interacting individuals, which may be called active particles [33]
Additional applications refer, among others, to modelling multicellular systems in biology [8, 18], swarm dynamics [14, 31, 34], living fluids [35], or vehicular traffic flows [9, 17, 24], while the interest of applying the methods of kinetic theory to model large systems is documented in the collection of surveys edited in [10]
Summary
This paper deals with the modelling of complex sociopsychological games and reciprocal feelings based on some conceptual developments of a new class of kinetic equations recently proposed in the literature to model the evolution of large systems of interacting individuals such that their microscopic state is defined by mechanical variables, and by additional variables, describing social and/or biological functions or behaviors. The guiding lines of the above mathematical approach is the derivation of an evolution equation for the statistical distribution over the microscopic state, which, as a particular case, may be related to a somehow intelligent, or at least organized, behavior of interacting individuals, which may be called active particles [33]. Interactions modify both the mechanical state (generally position and velocity) and the above introduced internal state; and those related to mechanical variables do not necessarily obey the laws of classical mechanics, considering that these may turn out to be themselves modified by what we have called an organized behavior.
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