LOCAL BIFURCATION OF CRITICAL PERIODS IN QUADRATIC-LIKE CUBIC SYSTEMS

Zhiheng Yu; Zhaoxia Wang

doi:10.11948/20190005

2019 Volume 9 Issue 5

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Zhiheng Yu, Zhaoxia Wang. LOCAL BIFURCATION OF CRITICAL PERIODS IN QUADRATIC-LIKE CUBIC SYSTEMS[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1901-1926. doi: 10.11948/20190005

Citation:

Zhiheng Yu, Zhaoxia Wang. LOCAL BIFURCATION OF CRITICAL PERIODS IN QUADRATIC-LIKE CUBIC SYSTEMS[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1901-1926. doi: 10.11948/20190005

LOCAL BIFURCATION OF CRITICAL PERIODS IN QUADRATIC-LIKE CUBIC SYSTEMS

Zhiheng Yu¹,
Zhaoxia Wang^2, ,

1.
School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
2.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Email address:wzx 0909@163.com (Z. Wang)
Fund Project: The authors were supported by National Natural Science Foundation of China (grant number 11501083 and 11701476) and the Fundamental Research Funds for the Central Universities (grant Number 2682018CX63)

Abstract

Abstract

In this paper, we investigate quadratic-like cubic systems having a center at $ O $ for the local bifurcation of critical periods. We provide an inductive algorithm to compute polynomials of periodic coefficients, find structures of solutions for systems of algebraic equations corresponding to weak centers of finite order, and derive conditions on parameters under which the considered equilibrium is a weak center of order $ k $, $ k = 0,1,2,3,4 $. Furthermore, we show that with appropriate perturbations, at most four critical periods bifurcate from the weak center of finite order, and we give conditions under which exactly $ k $ critical periods bifurcate from the center $ O $ for each integer $ k = 1,2,3,4 $.
- Quadratic-like cubic systems /
- critical period bifurcation /
- pseudo division /
- variety decomposition
MSC: 34C07, 34C23

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References

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