The mathematical analysis towards the dependence on the initial data for a discrete thermostatted kinetic framework for biological systems composed of interacting entities

Abstract

This paper is devoted to a mathematical proof of the continuous dependence on the initial data for the discrete thermostatted kinetic framework, for all T > 0. This is a versatile model for describing the time-evolution of a biological complex system which is composed by a large number of interacting entities, called active particles, and is subjected to an external force field due to the environment. A thermostat term is introduced in order to keep the 2nd-order moment of the system, corresponding to the physical global activation energy, constant in time. This model is expressed by a system of nonlinear ordinary differential equations with quadratic nonlinearity.