A rough system containing a parameter may become a non-rough system at a critical value of the parameter. Reduction of such a system to the ordinary (linear) normal form is impossible without special features (such as poles) in the change of variables. It is shown that a (nonlinear) generalization of the concept of the normal form allows us to use only smooth (by the independent variables and parameter) transformations. Integration of the proposed normal form is reduced to a series of quadratures. Such a formulation of the problem is caused by the need to study oscillatory biochemical systems, especially the variety of types of oscillatory excitation.

Mathematical modelling in actual problems of science and technics