THE SHAPE OF LIMIT CYCLES FOR A CLASS OF QUINTIC POLYNOMIAL DIFFERENTIAL SYSTEMS

Xuemei Wei; Shuliang Shui

doi:10.11948/2013021

2013 Volume 3 Issue 3

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Xuemei Wei, Shuliang Shui. THE SHAPE OF LIMIT CYCLES FOR A CLASS OF QUINTIC POLYNOMIAL DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2013, 3(3): 291-300. doi: 10.11948/2013021

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Xuemei Wei, Shuliang Shui. THE SHAPE OF LIMIT CYCLES FOR A CLASS OF QUINTIC POLYNOMIAL DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2013, 3(3): 291-300. doi: 10.11948/2013021

THE SHAPE OF LIMIT CYCLES FOR A CLASS OF QUINTIC POLYNOMIAL DIFFERENTIAL SYSTEMS

College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China

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Abstract

Abstract

We consider the problem of finding limit cycles for a class of quintic polynomial differential systems and their global shape in the plane. An answer to this problem can be given using the averaging theory. More precisely, we analyze the global shape of the limit cycles which bifurcate from a Hopf bifurcation and periodic orbits of the linear center ẋ=-y, ẏ=x, respectively.
- Limit cycles /
- quintic differential systems /
- Abelian equations /
- averaging methods
MSC: 34C25;34C23;34D10;34C29

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References

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