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In the last two decades the mathematical modeling of real-world complex systems has received much attention. These systems are composed by a high number of interacting entities which are able to express a specific strategy. In order to reduce complexity, the whole system is decomposed in different subsystems that are sets of heterogeneous entities having the ability of expressing the same function. The microscopic interactions among the functional subsystems generate the emerging behaviors that are typical of the complex systems. This paper is concerned with suitable developments of the methods of mathematical kinetic theory for active particles for the modeling of complex systems splitted in functional subsystems and constrained to maintain constant some macroscopic quantities.

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