HOPF BIFURCATION FOR PIECEWISE SMOOTH LIÉNARD SYSTEMS

Wenwen Hou; Dekai Zhu

doi:10.11948/20260328

2027 Volume 17 Issue 1

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Wenwen Hou, Dekai Zhu. HOPF BIFURCATION FOR PIECEWISE SMOOTH LIÉNARD SYSTEMS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 564-578. doi: 10.11948/20260328

Citation:

Wenwen Hou, Dekai Zhu. HOPF BIFURCATION FOR PIECEWISE SMOOTH LIÉNARD SYSTEMS[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 564-578. doi: 10.11948/20260328

HOPF BIFURCATION FOR PIECEWISE SMOOTH LIÉNARD SYSTEMS

Wenwen Hou^1, ,,
Dekai Zhu^2,

1.
Shanxi Key Laboratory of Cryptography and Data Security, School of Mathematical Sciences, Shanxi Normal University, Taiyuan, Shanxi 030031, China
2.
School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejiang 321004, China

Author Bio: Email: 19710578072@163.com(D. Zhu)
Corresponding author: Email: lebron_hww@163.com(W. Hou)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 12571187)

Abstract

Abstract

We consider a class of generalized Liénard systems and focus on the bifurcation of limit cycles near the origin as parameters vary. We derive the bifurcation function using a generalized polar coordinate transformation and analyze the cyclicity of the system at the origin, generalizing some known results. As an application, we discuss a special piecewise smooth system and study its cyclicity at the origin.
- Liénard system /
- Hopf bifurcation /
- cyclicity /
- piecewise smooth
MSC: 34C05, 34C07, 37G15

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References

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