Abstract
A bifurcation approach to analysis of divergent loss of stability of a trivial solution of a nonlinear dynamical system is presented. It is shown that the bifurcation set in the critical case of one zero root locally coincides with the discriminant set of a third-degree polynomial, which defines the set of stationary states of the system in neighborhood of symmetric solution of the system. This approach makes it possible to obtain conditions for safe-dangerous loss of stability of the symmetric solution, which are equivalent to the conditions of M. M. Bautin with minimum possible computational costs.
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