Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (2): 353-364.
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Xueli Jiang,Xuan Deng,Qiuhao Wen,Yanqin Xiong*()
Received:
2021-08-12
Online:
2022-04-26
Published:
2022-04-18
Contact:
Yanqin Xiong
E-mail:yqxiong@nuist.edu.cn
Supported by:
CLC Number:
Xueli Jiang,Xuan Deng,Qiuhao Wen,Yanqin Xiong. Limit Circle Bifurcations of Polynomial Differential System with Two Parallel Switch Straight Lines[J].Acta mathematica scientia,Series A, 2022, 42(2): 353-364.
1 | di Bernardo M, Budd C J, Champneys A R, Kowalczyk P. Piecewise Smooth Dynamical Systems, Theory and Applications. London: Springer-Verlag, 2008 |
2 | Budd C J. Non-smooth dynamical systems and the grazing bifurcation//Aston P J. Nonlinear Mathematics and Its Applications. Cambridge: Cambridge University Press, 1996: 219-235 |
3 | Filipov A F. Differential equations with discontionuous righthand sides. Netherlands: Kluwer Academic, 1988 |
4 |
Hilbert D . Mathematical Problems. Bull Amer Math, 1902, 8: 437- 479
doi: 10.1090/S0002-9904-1902-00923-3 |
5 |
Pi D , Zhang X . The sliding bifurcations in planar piecewise sooth differential systems. J Dyn Diff Equa, 2013, 25: 1001- 1026
doi: 10.1007/s10884-013-9327-0 |
6 |
Dankowicz H , Nordmark A B . On the origin and bifurcations of stick-slip oscillations. Physica D, 2000, 136: 280- 302
doi: 10.1016/S0167-2789(99)00161-X |
7 |
Feigin M I . Doubling of the oscillation period with C-bifurcations in piecewise-continuous systems. J Appl Math Mech, 1970, 34: 822- 830
doi: 10.1016/0021-8928(70)90064-X |
8 | Liu X , Han M . Bifurcation of limit cycles by perturbing piecewise Hamiltonian systems. Internat J Bifur Chaos, 2010, 5: 1- 12 |
9 |
Xiong Y , Han M . Limit cycle bifurcations in a class of perturbed piecewise smooth systems. Applied Mathematics and Computation, 2014, 242: 47- 64
doi: 10.1016/j.amc.2014.05.035 |
10 |
Liang F , Han M , Romanovskic V G . Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop. Nonlinear Analysis, 2012, 75: 4355- 4374
doi: 10.1016/j.na.2012.03.022 |
11 |
Hu N , Du Z . Bifurcation of periodic orbits emanated from a vertex in discontinuous planar systems. Commun Nonlinear Sci Numer Simulat, 2013, 18: 3436- 3448
doi: 10.1016/j.cnsns.2013.05.012 |
12 |
Xiong Y , Han M . Limit cycle bifurcations in discontinuous planar systems with multiple lines. Journal of Applied Analysis and Computation, 2020, 10: 361- 377
doi: 10.11948/20190274 |
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