Quasi-periodic dynamics

MAPS WITH QUASI-PERIODICITY OF DIFFERENT DIMENSION AND QUASI-PERIODIC BIFURCATIONS

The paper discusses the construction of convenient and informative three-dimensional mappings demonstrating the existence of 2-tori and 3-tori. The first mapping is obtained by discretizing the continuous time system – a generator of quasi-periodic oscillations. The second is obtained via discretization of the Lorentz-84 climate model. The third mapping was proposed in the theory of quasi-periodic bifurcations by Simo, Broer, Vitolo.

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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.

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