From microscopic to macroscopic descriptions of complex systems

doi:https://doi.org/10.1016/j.crme.2003.09.003

Article10.1016/j.crme.2003.09.003

From microscopic to macroscopic descriptions of complex systems

Mirosław Lachowicz-2003-10-21-Comptes Rendus Mécanique

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TL;DRAbstract

Complex systems that can be described at the macroscopic level in terms of bilinear ODEs or bilinear reaction–diffusion equations are considered. The corresponding microscopic description at the level of stochastically interacting entities is defined. The mathematical relationships between these two descriptions are formulated. The solutions of bilinear macroscopic equations are approximated by stochastic (linear) semigroups and the order of approximation is given.

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Complex systems that can be described at the macroscopic level in terms of bilinear ODEs or bilinear reaction–diffusion equations are considered. The corresponding microscopic description at the level of stochastically interacting entities is defined. The mathematical relationships between these two descriptions are formulated. The solutions of bilinear macroscopic equations are approximated by stochastic (linear) semigroups and the order of approximation is given.

Keywords

Bilinear interpolationMathematicsOdeComplex systemOrder (exchange)Pure mathematicsApplied mathematicsComputer science

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