FURTHER STUDIES ON LIMIT CYCLE BIFURCATIONS FOR PIECEWISE SMOOTH NEAR-HAMILTONIAN SYSTEMS WITH MULTIPLE PARAMETERS$ ^* $

Maoan Han; Shanshan Liu

doi:10.11948/20200003

2020 Volume 10 Issue 2

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Maoan Han, Shanshan Liu. FURTHER STUDIES ON LIMIT CYCLE BIFURCATIONS FOR PIECEWISE SMOOTH NEAR-HAMILTONIAN SYSTEMS WITH MULTIPLE PARAMETERS$ ^* $[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 816-829. doi: 10.11948/20200003

Citation:

Maoan Han, Shanshan Liu. FURTHER STUDIES ON LIMIT CYCLE BIFURCATIONS FOR PIECEWISE SMOOTH NEAR-HAMILTONIAN SYSTEMS WITH MULTIPLE PARAMETERS$ ^* $[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 816-829. doi: 10.11948/20200003

FURTHER STUDIES ON LIMIT CYCLE BIFURCATIONS FOR PIECEWISE SMOOTH NEAR-HAMILTONIAN SYSTEMS WITH MULTIPLE PARAMETERS$ ^* $

Maoan Han^1,2, ,,
Shanshan Liu²

1.
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China
2.
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

Corresponding author: Email address: mahan@shnu.edu.cn (M. Han)
Fund Project: The author was supported by National Natural Science Foundation of China (Nos. 11931016 and 11771296)

Abstract

Abstract

This paper investigates the limit cycle bifurcations for piecewise smooth near-Hamiltonian systems with multiple parameters. The formulas for the second and third term in expansions of the first order Melnikov function are derived respectively. The main results improve some known conclusions.
- Piecewise Hamiltonian systems /
- Melnikov function /
- limit cycle bifurcation
MSC: 37G15, 34C07

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References

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