| Abstract: |
| Multiscale systems often exhibit distinct yet related dynamical characteristics across different scales. One approach to exploring the relationship between dynamics at various spatial scales is through the concept of lumpability. This talk deals with exact lumpability of dynamical systems, namely the possibility of projecting the dynamics onto a smaller state space in which a self-contained dynamical description exists. This projection is also referred to as lumping, aggregation, or reduction in different contexts. We consider systems whose evolution is governed by bounded or unbounded linear operators on Banach spaces and derive conditions for lumpability in the language of semigroup theory. We further extend these results to nonlinear systems on finite-dimensional manifolds. Finally, we discuss lumpability within the framework of networks. |
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