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Asymptotics of Andronov–Hopf Dynamic Bifurcations

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We consider a system of two nonlinear differential equations with a slowly varying parameter μ = εt. For a frozen parameter μ = const the system has a focus type equilibrium state the stability of which changes when passing through the value μ = 0, i.e., we deal with an Andronov–Hopf bifurcation. Using the normal form method combined with the averaging method, we study asymptotics with respect to a small parameter ε → 0 for solutions having a narrow transient layer near the bifurcation point in the domain |εt| ≪ 1. We express the leading term of asymptotics in terms of the solution to the Bernoulli equation.

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  1. Institute of Mathematics, UFRC RAS, 112, Chernyshevsky St, Ufa, 450008, Russia

    L. A. Kalyakin

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  1. L. A. Kalyakin
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Correspondence to L. A. Kalyakin.

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Translated from Problemy Matematicheskogo Analiza 113, 2022, pp. 45-59.

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Kalyakin, L.A. Asymptotics of Andronov–Hopf Dynamic Bifurcations. J Math Sci 260, 756–773 (2022). https://doi.org/10.1007/s10958-022-05726-x

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