Density evolution by the low-field limit of kinetic frameworks with thermostat and mutations

•A system of integro-differential equations with quadratic nonlinearity.•Modeling of nonequilibrium complex systems with mutations.•Complex system decomposed into a finite number of functional subsystems.•Low-field scaling and asymptotic limit.•Macroscopic equations of local and global densities.

This paper is concerned with an asymptotic limit of a thermostatted kinetic framework which can be proposed for the modeling of complex biological and chemical systems where proliferative/destructive/mutative interactions and random velocity-jump processes occur. Specifically the macroscopic equations fulfilled by the local and global densities of the system are obtained by performing an asymptotic limit of a low-field rescaling of a kinetic framework with a thermostat and mutative interactions.