BIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEM

Yusen Wu; Ming Zhang; Jinxiu Mao

doi:10.11948/20190424

2020 Volume 10 Issue 6

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Yusen Wu, Ming Zhang, Jinxiu Mao. BIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEM[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2575-2591. doi: 10.11948/20190424

Citation:

Yusen Wu, Ming Zhang, Jinxiu Mao. BIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEM[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2575-2591. doi: 10.11948/20190424

BIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEM

1.
School of Statistics, Qufu Normal University, Qufu, Shandong, 273165, China
2.
School of Mathematics and Statistics, Linyi University, Linyi, Shandong, 276005, China
3.
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, China

Corresponding author: Email address:wuyusen621@126.com(Y. Wu)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 12071198)

Abstract

Abstract

In this paper, we characterize local behavior of an isolated nilpotent critical point for a class of septic polynomial differential systems, including center conditions and bifurcation of limit cycles. With the help of computer algebra system-MATHEMATICA 12.0, the first 15 quasi-Lyapunov constants are deduced. As a result, necessary and sufficient conditions of such system having a center are obtained. We prove that there exist 16 small amplitude limit cycles created from the third-order nilpotent critical point. And then we give a lower bound of cyclicity of third-order nilpotent critical point for septic Lyapunov systems.
- Third-order nilpotent critical point /
- center-focus problem /
- bifurcation of limit cycles /
- Quasi-Lyapunov constant
MSC: 34C05, 37G15

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References

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