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.
Citation: Marco Menale, Bruno Carbonaro. The mathematical analysis towards the dependence on the initial data for a discrete thermostatted kinetic framework for biological systems composed of interacting entities[J]. AIMS Biophysics, 2020, 7(3): 204-218. doi: 10.3934/biophy.2020016
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.
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