The talk includes fragmentarily some aspects of the analysis of a few Lorenz-like systems (3D symmetrical and asymmetrical classical models, 14D model, Shimizu-Marioka system), in particular, details of detection of the region of existence of the Lorenz attractor in the parameter space. The idea begins mainly with selection of codimension-two homoclinic bifurcations.

A recent result on a "blue-sky catastrophe"bifurcation of codimension one for periodic orbits and its connection with dynamics in biophysical models are also discussed.

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