BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTER AT INFINITY FOR A CLASS OF DIFFERENTIAL SYSTEMS

Wentao Huang; Yirong Liu; Weinian Zhang

doi:10.11948/2011027

2011 Volume 1 Issue 3

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Wentao Huang, Yirong Liu, Weinian Zhang. BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTER AT INFINITY FOR A CLASS OF DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2011, 1(3): 397-410. doi: 10.11948/2011027

Citation:

Wentao Huang, Yirong Liu, Weinian Zhang. BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTER AT INFINITY FOR A CLASS OF DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2011, 1(3): 397-410. doi: 10.11948/2011027

BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTER AT INFINITY FOR A CLASS OF DIFFERENTIAL SYSTEMS

1 School of Mathematics and Computing Science, Guilin University of Electronic, Technology, Guilin, 541004, P. R. China;
2 School of Mathematical Science, Central South University, Changsha 410083, P. R. China;
3 School of Mathematics Science, Sichuan University, Chengdu 610064, P. R. China

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Abstract

Abstract

In this paper, we study a seventh degree polynomial differential system with full linear terms and cubic terms. The conditions of infinity to be a center and to be a fine focus of the highest order are given and it is proved that this system has eight limit cycles in the neighborhood of infinity. Moreover, the conditions of infinity to be an isochronous center for a rational system associated the seventh degree polynomial differential system are obtained.
- Infinity /
- Limit cycle /
- Isochronous center /
- Singular point value /
- Period constant
MSC: 34C07

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References

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