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Hopf bifurcation at a degenerate singular point In 3-dimensional vector field.(English)Zbl 07907314

Summary: The work of this paper focuses on investigating limit cycle bifurcation for a degenerate singular point in 3-Dimensional vector fields. By making two appropriate transformations and making use of singular values methods to compute focal values carefully, we give the expressions of the first five Lyapunov constants at the origin that is a degenerate singular point. Moreover, we obtain the considered system can bifurcate 5 limit cycles near the origin. In terms of results on limit cycle bifurcation from degenerate singular point in 3-Dimensional vector field, it is less seen in published references..

MSC:

34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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