平面分片光滑系统中同宿环的稳定性

Stability of Homoclinic Cycles in Planar Piecewise Smooth Systems

ZHENG Dan, DONG Xianfeng, SUN Hui qun, YU Shi, ZHANG Ran

College of Mathematics, Jilin University, Changchun 130012, China

Received:2006-10-13 Revised:1900-01-01 Online:2007-05-26 Published:2007-05-26
Contact: ZHANG Ran

Abstract

Abstract: The stability of homoclinic cycles in planar piecewise smooth systems was studied. A criterion for judging the stability of the homoclinic cycle was presented under the condition of saddle quantity is nontrivial. It was proved that the stability of the homoclinic cycle is only dependent on the sign of the saddle quantity. A numerical experiment was carried out to illustrate the theoretical result.

Key words: piecewise smooth system, homoclinic cycle, stability, saddle quantity

CLC Number:

O241.81

ZHENG Dan, DONG Xianfeng, SUN Hui qun, YU Shi, ZHANG Ran. Stability of Homoclinic Cycles in Planar Piecewise Smooth Systems[J].J4, 2007, 45(03): 349-352.

[1]	WANG Han, LI Huilai, LI Wenxuan. Dynamic Behaviors of a Measles Model Based on Secondary Vaccine Failure [J]. Journal of Jilin University Science Edition, 2021, 59(5): 1003-1008.
[2]	MA Xiaoqi, ZHAO Zhitao. Dynamic Analysis of a Class of Plant-Herbivore Diffusion System [J]. Journal of Jilin University Science Edition, 2021, 59(5): 1057-1065.
[3]	QIAN Rong, XIAO Min, WANG Lu. Stability Analysis of Fractional-Order SIR Epidemic Models with Different Orders [J]. Journal of Jilin University Science Edition, 2021, 59(4): 796-806.
[4]	SONG Xiangwei , DOU Xinyue, SHA Yue, LUO Rui, WANG Xueli. Effect of Helical Structure on Bioactivity and Stability of Exendin-4 [J]. Journal of Jilin University Science Edition, 2021, 59(4): 988-992.
[5]	ZHAN Huashui, YUAN Hongjun. Uniqueness of Solutions to Degenerate Parabolic Equation with Variable Exponents [J]. Journal of Jilin University Science Edition, 2021, 59(1): 1-6.
[6]	LI Hui, CHU Huilian, ZHAO Qiliang, LIU Yue. Synchronous Circuit Design of Brushless DC Motor [J]. Journal of Jilin University Science Edition, 2021, 59(1): 162-167.
[7]	BAO Xuezhong, HU Lin, GUO Huiqing. Convergence and Stability of Balanced Methods for Stochastic Variable Delay Differential Equations [J]. Journal of Jilin University Science Edition, 2020, 58(6): 1345-1356.
[8]	ZHAO Yanxia, YANG He. Exp-Type Ulam-Hyers Stability of Fractional Impulsive Integro-Differential Equations in Banach Spaces [J]. Journal of Jilin University Science Edition, 2020, 58(5): 1055-1065.
[9]	CAO Mingyuan, YANG Yueting, ZHANG Yanyu, HUANG Qingdao. Dynamic Properties of Nonlinear DifferenceEquation with Periodic Coefficients [J]. Journal of Jilin University Science Edition, 2020, 58(3): 457-462.
[10]	LI Wenxuan, LI Huilai, ZHAO Yanjun. A Class of SIRS Epidemic Model Based on Psychology Effect [J]. Journal of Jilin University Science Edition, 2020, 58(3): 513-517.
[11]	LI Xiaoping, HUANG Rong, LI Huilai. Dynamic Analysis of Epidemic Model with Vertical Transmission [J]. Journal of Jilin University Science Edition, 2020, 58(3): 569-574.
[12]	ZHAO Zhixin, TANG Hui. Stability Analysis of Repairable Systemwith Two Different Failure Modes [J]. Journal of Jilin University Science Edition, 2020, 58(2): 285-292.
[13]	YU Huanhuan, AN Xinlei, LU Zhengyu, WANG Wenjing. Stability and Hopf Bifurcation Analysis of FluxCoupled Neuron Model [J]. Journal of Jilin University Science Edition, 2020, 58(2): 388-396.
[14]	SUN Mingfen, REN Xiu’e, LIAO Zepeng, WANG Hongyan, HE Wenjun, MENG Fanxin. Effects of Isocyanate Index on Properties of Polyurethane Powder Adhesives [J]. Journal of Jilin University Science Edition, 2020, 58(1): 171-176.
[15]	LI Xue, XU Xu. Stability of TwoDimensional Complex Oscillator Networks with Time Delay [J]. Journal of Jilin University Science Edition, 2019, 57(3): 571-573.

Stability of Homoclinic Cycles in Planar Piecewise Smooth Systems

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 1