The Simplest Map with Three-Frequency Quasi-Periodicity and Quasi-Periodic Bifurcations

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 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 nonautonomous model is carried out.