ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION

Jihua Yang

doi:10.11948/20190220

2020 Volume 10 Issue 6

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Jihua Yang. ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2362-2380. doi: 10.11948/20190220

Citation:

Jihua Yang. ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2362-2380. doi: 10.11948/20190220

ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION

Jihua Yang^1, ,

1.
School of Mathematics and Computer Science, Ningxia Normal University, Xueyuan Road, 756000 Guyuan, China

Corresponding author: Email: jihua1113@163.com(J. Yang)
Fund Project: The author was supported by National Natural Science Foundation of China(11701306), Construction of First-class Disciplines of Higher Education of Ningxia(Pedagogy)(NXYLXK2017B11), Natural Science Foundation of Ningxia (2019AAC03247) and Higher Education Science and Technology Program of Ningxia(NGY2020074)

Abstract

Abstract

This paper deals with the problem of limit cycle bifurcations for a piecewise smooth Hamilton system with two straight lines of separation. By analyzing the obtained first order Melnikov function, we give upper and lower bounds of the number of limit cycles bifurcating from the period annulus between the origin and the generalized homoclinic loop. It is found that the first order Melnikov function is more complicated than in the case with one straight line of separation and more limit cycles can be bifurcated.
- Piecewise smooth Hamilton system /
- limit cycle /
- generalized homoclinic loop /
- Melnikov function
MSC: 34C07, 34C05

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References

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