Abstract
Possibilities of catastrophes existence in the linearized model with two degree of freedom, hav- ing the solution of steady focus type, were studied. The essence of catastrophes is based on the criteria of extermination of fluctuation types near stationary points of phase space. Irregularities of self– oscillating process of cell metabolism, which have the same roots, are the cause of many illnesses of living organisms. A stationary set of the main parameters of the linearized model of interaction with two degree of freedom is presented. There is a strong dependence both on the original nonlinearity and the set of stationary points of the problem. The model can be used for forecasting of evolution of interaction and coexistence of concurrent systems.