BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES

Lijuan Sheng; Maoan Han

doi:10.11948/20190342

2019 Volume 9 Issue 6

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Lijuan Sheng, Maoan Han. BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2482-2495. doi: 10.11948/20190342

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Lijuan Sheng, Maoan Han. BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2482-2495. doi: 10.11948/20190342

BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES

Lijuan Sheng¹,
Maoan Han^2,1, ,

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

Corresponding author: Email address:mahan@shnu.edu.cn(M. Han)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 11801372, 11931016, 11771296, 11971317 and 11871042)

Abstract

Abstract

We concern the number of limit cycles of a polynomial system with degree nine. We prove that under different conditions, the system can have 12 and 20 limit cycles bifurcating from a compound loop with five saddles. Our method relies upon the Melnikov function method and the method of stability-changing of a double homoclinic loop proposed by the authors[J. Yang, Y. Xiong and M. Han, Nonlinear Anal-Theor., 2014, 95, 756-773].
- Limit cycle /
- bifurcation /
- Melnikov function /
- homoclinic loop
MSC: 34C07

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References

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