SECOND ORDER MELNIKOV FUNCTIONS FOR PLANAR PIECEWISE SMOOTH INTEGRABLE NON-HAMILTONIAN SYSTEMS WITH MULTIPLE ZONES AND APPLICATION

Li Zou; Liqin Zhao

doi:10.11948/20230136

2023 Volume 13 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(5): 2995-3025

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Li Zou, Liqin Zhao. SECOND ORDER MELNIKOV FUNCTIONS FOR PLANAR PIECEWISE SMOOTH INTEGRABLE NON-HAMILTONIAN SYSTEMS WITH MULTIPLE ZONES AND APPLICATION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2995-3025. doi: 10.11948/20230136

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Li Zou, Liqin Zhao. SECOND ORDER MELNIKOV FUNCTIONS FOR PLANAR PIECEWISE SMOOTH INTEGRABLE NON-HAMILTONIAN SYSTEMS WITH MULTIPLE ZONES AND APPLICATION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2995-3025. doi: 10.11948/20230136

SECOND ORDER MELNIKOV FUNCTIONS FOR PLANAR PIECEWISE SMOOTH INTEGRABLE NON-HAMILTONIAN SYSTEMS WITH MULTIPLE ZONES AND APPLICATION

Li Zou^1,,
Liqin Zhao^1, ,

1.
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Author Bio: Email: lizou@mail.bnu.edu.cn(L. Zou)
Corresponding author: Email: zhaoliqin@bnu.edu.cn(L. Zhao)

Abstract

Abstract

In this paper, we study the expressions of the second order Melnikov functions for planar piecewise smooth integrable non-Hamiltonian systems with m(∈ $\mathbb{N}$) zones separated by half straight lines through the origin under the piecewise perturbations. As an application, it is proved that there exists a planar piecewise quadratic system having at least 8 limit cycles near the origin.
- Piecewise smooth integrable non-Hamiltonian system /
- second order Melnikov function /
- limit cycle /
- bifurcation
MSC: 34C05,34C07

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References

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