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Principal asymptotics in the problem on the Andronov-Hopf bifurcation and their applications. (English. Russian original) Zbl 1391.34076
Differ. Equ. 53, No. 12, 1578-1594 (2017); translation from Differ. Uravn. 53, No. 12, 1627-1642 (2017).
The Andronov-Hopf bifurcation is an important problem in the theory of nonlinear oscillations. In this paper, the authors propose new asymptotic formulas for studying the Andronov-Hopf bifurcation in terms of the original equations. The formulas are useful both for approximate bifurcation studies and in the stability analysis of the corresponding solutions. The approach permits one to study not only problems on bifurcations of codimension one but also some problems on bifurcations of codimension two. This paper proposes a new approach to analyze the bifurcation of a limit cycle in systems with homogeneous nonlinearities.

MSC:
34C23 Bifurcation theory for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
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