Singularities of transition processes  in dynamical systems:     Qualitative theory of critical delays

Gorban, Alexander N.

doi:10.58997/ejde.mon.05

Cited by 5 publications

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Basic Types of Coarse-Graining

Gorban

Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

View full text Add to dashboard Cite

Summary. We consider two basic types of coarse-graining: the Ehrenfests' coarsegraining and its extension to a general principle of non-equilibrium thermodynamics, and the coarse-graining based on uncertainty of dynamical models and ε-motions (orbits). Non-technical discussion of basic notions and main coarse-graining theorems are presented: the theorem about entropy overproduction for the Ehrenfests' coarse-graining and its generalizations, both for conservative and for dissipative systems, and the theorems about stable properties and the Smale order for ε-motions of general dynamical systems including structurally unstable systems. Computational kinetic models of macroscopic dynamics are considered. We construct a theoretical basis for these kinetic models using generalizations of the Ehrenfests' coarsegraining. General theory of reversible regularization and filtering semigroups in kinetics is presented, both for linear and non-linear filters. We obtain explicit expressions and entropic stability conditions for filtered equations. A brief discussion of coarse-graining by rounding and by small noise is also presented.

show abstract