Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system

Li Feng, Liu Yirong and Li Hongwei

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 12, 2595-2607

Abstract: In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of septic polynomial differential systems are investigated. With the help of computer algebra system MATHEMATICA, the first 13 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The result that there exist 13 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for septic Lyapunov systems.

Keywords: Three-order nilpotent critical point; Center-focus problem; Bifurcation of limit cycles; Quasi-Lyapunov constant (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:12:p:2595-2607

DOI: 10.1016/j.matcom.2011.05.001

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