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Finite-time attractivity and bifurcation for nonautonomous differential equations. (English) Zbl 1213.34070
The aim of the paper is to introduce nonautonomous and finite-time versions of central concepts from the theory of dynamical systems such as attractivity and bifurcation. The discussion includes an appropriate spectral theory for linear systems as well as finite-time analogues of the well-known transcritical and pitchfork bifurcations. The introduced notions are illustrated by several examples.

MSC:
34D45 Attractors of solutions to ordinary differential equations
34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
37B55 Topological dynamics of nonautonomous systems
37G35 Dynamical aspects of attractors and their bifurcations
34C23 Bifurcation theory for ordinary differential equations
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