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Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system. (English) Zbl 1242.34050

Center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of septic polynomial differential systems are investigated. By means of the computer algebra system MATHEMATICA, the first 13 quasi-Lyapunov constants are deduced. Necessary and sufficient center conditions are obtained. It is proved that there exist 13 small amplitude limit cycles bifurcating from the third-order nilpotent critical point.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations

Software:

Mathematica
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Full Text: DOI

References:

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