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Asymptotic behavior of solutions of system with critical variables in the case of two pairs of purely imaginary roots. (Russian. English summary) Zbl 1260.34102
Summary: This paper is focused on the study of the critical case of the stability theory under the assumption that the matrix of the linear approximation has two pairs of purely imaginary eigenvalues. The main result provides an asymptotic estimate of the solutions in the case of stability with respect to third-order forms. The Lyapunov function for the system with stable and critical components is constructed.
MSC:
34D05 Asymptotic properties of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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