Abstract
The aim of this article 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 bifurcation.
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This work is dedicated to the memory of my supervisor Professor Bernd Aulbach
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Rasmussen, M. Finite-time attractivity and bifurcation for nonautonomous differential equations. Differ Equ Dyn Syst 18, 57–78 (2010). https://doi.org/10.1007/s12591-010-0009-7
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DOI: https://doi.org/10.1007/s12591-010-0009-7
Keywords
- Attractor
- dichotomy
- dichotomy spectrum
- finite-time dynamics
- nonautonomous differential equation
- nonautonomous bifurcation
- pitchfork bifurcation
- repeller
- transcritical bifurcation