ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


torus

Autonomous generator of quasiperiodic oscillations

A simple autonomous three-dimensional system is introduced that demonstrates quasiperiodic self-oscillations and has as attractor a two-dimensional torus. The computing illustrations of quasiperiodic dynamics are presented: phase portraits, Fourie spectrums, graphics of Lyapunov exponents. The existing of Arnold tongues on the parametric plane and transition from quasiperiodic dynamics to chaos through destruction of invariant curve in the Poincare section are shown.

Four-dimensional system with torus attractor birth via saddle-node bifurcation of limit cycles in context of family of blue sky catastrophes

A new four-dimensional model with quasi-periodic dynamics is suggested. The torus attractor originates via the saddle-node bifurcation, which may be regarded as a member of a bifurcation family embracing different types of blue sky catastrophes. Also the torus birth through the Neimark-Sacker bifurcation occurs in some other region of the parameter space.