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arXiv · 1602.05760

The simplest map with three-frequency quasi-periodicity and quasi-periodic bifurcations

A. P. Kuznetsov·Yu. V. Sedova
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Abstract

We propose a new three-dimensional map that demonstrates the two- and three-frequency quasi-periodicity. For this map all basic quasi-periodic bifurcations are possible. The study was realized by using method of Lyapunov charts completed by plots of Lyapunov exponents, phase portraits and bifurcation trees illustrating the quasi-periodic bifurcations. The features of the three-parameter structure associated with quasi-periodic Hopf bifurcation are discussed. The comparison with non-autonomous model is carried out.

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A. P. Kuznetsov, Yu. V. Sedova. 2016-02-18. The simplest map with three-frequency quasi-periodicity and quasi-periodic bifurcations. https://doi.org/10.1142/s0218127416300196

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