strange nonchaotic attractor.

Processes of the El Ni  ̃no – Southern Oscillation (ENSO) are investigated based on the mathematical theory of the so-called the strange nonchaotic attractor (SNA) in the quasiperiodically forced dynamic systems, and using the sea surface temperature and the atmospheric sea-level pressure data for the 1870–2014 year period.

The transition to chaos through the destruction of three-dimensional torus is studied in a nonautonomous system with quasi-periodic impact as example. Analysis is carried out of the influence both of additive noise and frequency fluctuations impact on the stability of three-dimensional torus. It is shown that under the influence of additive noise and frequency fluctuations impact Lyapunov exponent remains negative. This allows to conclude that in this model three-dimensional torus is structurally stable in contrast to theautonomous system.