Been WAITING for someone to write about this. Here’s hoping I understand it.
Basically, it applies the notions of autonomous chaotic systems but applies them to those that change over time and are dependent upon time. this should be a far more realistic treatment of chaotic systems as real systems, particularly biological and chemical, aren’t steady-state nor entirely random and yet we tend to model them as such.
[BOOK] Attractivity and bifurcation for nonautonomous dynamical systems
M Rasmussen – 2007 – books.google.com
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces …
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