Catastrophe hyperbolic umbilic

Elementary catastrophes of two variables also have common names. In order D4, D4 +, ...,E6 these are elliptic umbilic, hyperbolic umbilic, parabolic umbilic, second elliptic umbilic, second hyperbolic umbilic and symbolic umbilic catastrophes. 

The description of catastrophes corresponding to functions of two variables will be begin with a hyperbolic umbilic catastrophe Z)4+, which is represented by the potential function... 

On the other hand, in connection with theoretical analysis of the problems related to scattering of atoms on crystals and in the model of scattering of atoms on rigid rotators appears the canonical integral (3.25) containing the potential function F(x c) of the elementary catastrophe of hyperbolic umbilic (D4+) F(x c) = x3 + y3 + axy + bx + cy. 

Remarkably, the hierarchy (3.257) starts with the QSAR model, which is revealed to be at the top of the validated catastrophe models with statistical performance even higher than through the predicted equation of Table 3.23 and the trial set of Table 3.21. Moreover, the QSAR-II model involves parameters (LogP H) that are followed by the hyperbolic umbilic (HU) model in terms of (LogP POL) parameters, in this way... 

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