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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:
34C05Location of integral curves, singular points, limit cycles (ODE)
34C07Theory of limit cycles of polynomial and analytic vector fields
34C23Bifurcation (ODE)
34-04Machine computation, programs (ordinary differential equations)
Software:
Mathematica
References:
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