PHASE PORTRAITS OF <i>Z</i><sub>7</sub>-EQUIVARIANT SEXTIC HAMILTONIAN SYSTEM

Bin Luo; Yuhai Wu; Li Yang

doi:10.11948/2014007

2014 Volume 4 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2014 > 4(2): 139-149

Next Article Previous Article

Bin Luo, Yuhai Wu, Li Yang. PHASE PORTRAITS OF Z7-EQUIVARIANT SEXTIC HAMILTONIAN SYSTEM[J]. Journal of Applied Analysis & Computation, 2014, 4(2): 139-149. doi: 10.11948/2014007

Citation:

Bin Luo, Yuhai Wu, Li Yang. PHASE PORTRAITS OF Z₇-EQUIVARIANT SEXTIC HAMILTONIAN SYSTEM[J]. Journal of Applied Analysis & Computation, 2014, 4(2): 139-149. doi: 10.11948/2014007

PHASE PORTRAITS OF Z₇-EQUIVARIANT SEXTIC HAMILTONIAN SYSTEM

Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Fund Project:

Abstract

Abstract

In this paper, a sextic Hamiltonian system with Z₇-equivariant property is considered. Using the methods of qualitative analysis of differential equations, bifurcations of the above system are analyzed, the phase portraits of the system are classified and the corresponding representative orbits are shown by Maple software.
- Sextic Hamiltonian system /
- Z₇-equivariant /
- qualitative analysis /
- phase portraits /
- bifurcations
MSC: 34C07;34C23;34C37;37G15

FullText(HTML)

References

[1]	Longwei Chen and Jianguo Ning, Phase portraits of Z6-equivariant system, Mathematics in Practice and Theory, 2(2005), 140-143. Google Scholar
[2]	Guowei Chen and Xinan Yang, Topological sorting of phase portraits of quintic Hamiltonian system, Acta Mathematica Scientia, 6(2004), 737-751. Google Scholar
[3]	Xinyu Fang, Wentao Huang and Aiyong Chen, The number of limit cycles for a class of quartic Hamiltonion system, Acta Scientiarum naturalium universitatis Sunyatsent, 2(2012), 35-39. Google Scholar
[4]	Yi Huang and Yuhai Wu, Phase portraits of a class of Z5-invariant quartic Hamiltonian system, Journal of Gansu Lianhe University, 6(2011), 5-10. Google Scholar
[5]	Rasool Kazemi and Hamid R.Z.Zangeneh, Bifurcation of limit cycles in small pertur-bations of a hyper-elliptic Hamiltonian system with two nilpotent saddles, Journal of Applied Analysis and Computation, 4(2013), 395-413. Google Scholar
[6]	Yanmei Li, Phase portraits of a class of Z3-invariant quiatic Hamiltonian system, Journal of Yunnan Normal University, 6(2003), 5-7. Google Scholar
[7]	Jibin Li and Fenquan Chen, Chaos, Method of Melnikov and Its New Development, Beijing, Science Press, 2012. Google Scholar
[8]	Noel G. Lloyd and Jane M. Pearson, A cubic dierential system with nine limit cycles, Journal of Applied Analysis and Computation, 3(2013), 293-304. Google Scholar
[9]	Xuemei Wei and Shu liang Shui, The shape of limit cycles for a class of quintic polynomial differential systems, Journal of Applied Analysis and Computation, 3(2013), 291-300. Google Scholar
[10]	Zhifen Zhang, Tongren Ding, etc, Qualitative Theories of Differential Equations, Beijing, Science Press, 1997(Edition 2). Google Scholar