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Zbl 1213.34070
Rasmussen, Martin
Finite-time attractivity and bifurcation for nonautonomous differential equations. (English)
[J] Differ. Equ. Dyn. Syst. 18, No. 1-2, 57-78 (2010). ISSN 0971-3514; ISSN 0974-6870/e

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.
[Eugene Ershov (St. Petersburg)]

MSC 2000:: *34D45 Attractors
34D09 Dichotomy, trichotomy
37B55 Nonautonomous dynamical systems
37G35 Attractors and their bifurcations
34C23 Bifurcation (periodic solutions)

Keywords: attractor; dichotomy; dichotomy spectrum; finite-time dynamics; nonautonomous differential equation; nonautonomous bifurcation; pitchfork bifurcation; repeller; transcritical bifurcation

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