Dynamical properties of two simple models derived from the equations of physics of the atmosphere are investigated in this paper. Attention was paid to the structure of attraction sets (especially to their borders) of the attractors existing in the models. The influence of precision of the integrating procedures' on some of the attractors identification was investigated. The mechanism of destroying a strange attractor (by the nonlinear resonance) in a Lorenz system with thermal forcing was found.
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