Complex integrability and linearizability of cubic Z2-equivariant systems with two 1:q resonant singular points

Li, Feng; Liu, Yuanyuan; Yu, Pei; Wang, Jinliang

doi:10.1016/j.jde.2021.08.015

Cited by 14 publications

(1 citation statement)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…then the switching system (1) is Z 2 -equivariant. Li and his collaborators have made a series of achievements in the study of dynamics such as limit cycles and integrability for Z 2 -equivariant planar system, as evidenced by references [13][14][15][16]. In addition, there have been notable advancements in the application research of bifurcation of limit cycles in symmetric systems.…”

Section: Introductionmentioning

confidence: 99%

Limit Cycles and Local Bifurcation of Critical Periods in a Class of Switching Z2 Equivariant Quartic System

Yang,

Liu,

2024

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

In this paper, the limit cycles and local bifurcation of critical periods for a class of switching Z2 equivariant quartic system with two symmetric singularities are investigated. First, through the computation of Lyapunov constants, the conditions of the two singularities to become the centers are determined. Then, we prove that there are at most 18 limit cycles with a distribution pattern of 9-9 around the two symmetric singular points of the system. Numerical simulation is conducted to validate the obtained results. Furthermore, by calculating the period constants, we determine the conditions for the critical point to be a weak center of finite order. Finally, the number of local critical periods that bifurcate from the equilibrium point under the center conditions is discussed. This study presents the first example of a quartic switching smooth system with 18 limit cycles and 4 local critical periods bifurcating from two symmetric singular points.

show abstract

Section: Introductionmentioning

confidence: 99%

Limit Cycles and Local Bifurcation of Critical Periods in a Class of Switching Z2 Equivariant Quartic System

Yang,

Liu,

2024

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

show abstract

The Integrability and Linearizability of Cubic $$Z_2$$-Equivariant Systems with Two 1:$$-q$$ Resonant Saddle Points

Wang,

Liu

2024

Qual. Theory Dyn. Syst.

View full text Add to dashboard Cite

Integrability and non-linearizability of weak saddles in a cubic Kolmogorov model

Zhang

2021

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

Complex integrability and linearizability of cubic Z2-equivariant systems with two 1:q resonant singular points

Cited by 14 publications

References 27 publications

Limit Cycles and Local Bifurcation of Critical Periods in a Class of Switching Z2 Equivariant Quartic System

Limit Cycles and Local Bifurcation of Critical Periods in a Class of Switching Z2 Equivariant Quartic System

The Integrability and Linearizability of Cubic $$Z_2$$-Equivariant Systems with Two 1:$$-q$$ Resonant Saddle Points

Integrability and non-linearizability of weak saddles in a cubic Kolmogorov model

Contact Info

Product

Resources

About