A Note on the Kaplan–Yorke Dimension
article
In nonlinear dynamics, multifrequency oscillations arise in many applications of various disciplines. The mathematical equations describing these oscil lations contain parameters that upon changing can display many different types of bifurcations; see for instance [Kuznetsov, 2023]. A remarkable phenomenon is the emergence of chaotic motion that is often characterized by geo metric structures. There are differences between conservative and dissipative systems, we will focus here on the latter. One has identified various sce narios leading to chaos as a prominent one period doubling. In this case, one starts with a periodic solution for certain parameter values. Changing the parameters leads to a periodic solution with double period, changing again redoubles the period and so on ad infinitum. In the limit of parameter changes, one has a bifurcation sequence of parameters pro ducing chaotic motion. We use an illustration of system NE9 from [Bakri & Verhulst, 2022]. In Fig. 1, we show the period-doubling sequence on the left and the result ing chaotic attractor on the right.
TNO Identifier
1017059
Source
International Journal of Bifurcation and Chaos, pp. 1-5.
Pages
1-5
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