In the discrete thermostatted kinetic theory: Proliferations, mutations and microscopic agents}

Abstract

This paper is concerned with the modeling of complex living systems composed of active particles able to interact with each other and with the surrounding environment. Specifically the discrete thermostatted kinetic theory for active particles is generalized by extending the role of nonconservative interactions and by introducing the role of mutations. In particular the classical proliferation/destruction operator is generalized in order to take into consideration the role of nonlinear interactions, namely the dependence on the distribution functions and their moments. The natural birth and death events are recovered included the logistic growth rate. Finally the role of the outer environment is taken into consideration by introducing microscopic external agents. New thermostat operators are presented whose structures augment the degree of nonlinearity of the evolution equations. The different Cauchy problems are established and future research perspectives are discussed in the whole paper.