-
Previous Article
Eigenmodes and eigenfrequencies of vibrating elliptic membranes: a Klein oscillation theorem and numerical calculations
- CPAA Home
- This Issue
- Next Article
Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes
1. | Institute of Mathematics, Bulgarian Academy of Sciences, Bl. 8, 1113 Sofia, Bulgaria |
2. | LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China |
3. | Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China |
[1] |
Linping Peng, Yazhi Lei. The cyclicity of the period annulus of a quadratic reversible system with a hemicycle. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 873-890. doi: 10.3934/dcds.2011.30.873 |
[2] |
Yi Shao, Yulin Zhao. The cyclicity of the period annulus of a class of quadratic reversible system. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1269-1283. doi: 10.3934/cpaa.2012.11.1269 |
[3] |
Ricardo M. Martins, Otávio M. L. Gomide. Limit cycles for quadratic and cubic planar differential equations under polynomial perturbations of small degree. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3353-3386. doi: 10.3934/dcds.2017142 |
[4] |
Linping Peng, Zhaosheng Feng, Changjian Liu. Quadratic perturbations of a quadratic reversible Lotka-Volterra system with two centers. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4807-4826. doi: 10.3934/dcds.2014.34.4807 |
[5] |
Guilin Ji, Changjian Liu. The cyclicity of a class of quadratic reversible centers defining elliptic curves. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021299 |
[6] |
Jaume Llibre, Yilei Tang. Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. Discrete and Continuous Dynamical Systems - B, 2019, 24 (4) : 1769-1784. doi: 10.3934/dcdsb.2018236 |
[7] |
Adriana Buică, Jaume Giné, Maite Grau. Essential perturbations of polynomial vector fields with a period annulus. Communications on Pure and Applied Analysis, 2015, 14 (3) : 1073-1095. doi: 10.3934/cpaa.2015.14.1073 |
[8] |
Bourama Toni. Upper bounds for limit cycle bifurcation from an isochronous period annulus via a birational linearization. Conference Publications, 2005, 2005 (Special) : 846-853. doi: 10.3934/proc.2005.2005.846 |
[9] |
B. Coll, Chengzhi Li, Rafel Prohens. Quadratic perturbations of a class of quadratic reversible systems with two centers. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 699-729. doi: 10.3934/dcds.2009.24.699 |
[10] |
Haihua Liang, Yulin Zhao. Quadratic perturbations of a class of quadratic reversible systems with one center. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 325-335. doi: 10.3934/dcds.2010.27.325 |
[11] |
G. Chen, C. Li, C. Liu, Jaume Llibre. The cyclicity of period annuli of some classes of reversible quadratic systems. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 157-177. doi: 10.3934/dcds.2006.16.157 |
[12] |
Yulin Zhao. On the monotonicity of the period function of a quadratic system. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 795-810. doi: 10.3934/dcds.2005.13.795 |
[13] |
Ai Ke, Maoan Han, Wei Geng. The number of limit cycles from the perturbation of a quadratic isochronous system with two switching lines. Communications on Pure and Applied Analysis, 2022, 21 (5) : 1793-1809. doi: 10.3934/cpaa.2022047 |
[14] |
Jaume Llibre, Dana Schlomiuk. On the limit cycles bifurcating from an ellipse of a quadratic center. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1091-1102. doi: 10.3934/dcds.2015.35.1091 |
[15] |
José Luis Bravo, Manuel Fernández, Ignacio Ojeda, Fernando Sánchez. Uniqueness of limit cycles for quadratic vector fields. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 483-502. doi: 10.3934/dcds.2019020 |
[16] |
Jaume Llibre, Claudia Valls. Algebraic limit cycles for quadratic polynomial differential systems. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2475-2485. doi: 10.3934/dcdsb.2018070 |
[17] |
Hong Li. Bifurcation of limit cycles from a Li$ \acute{E} $nard system with asymmetric figure eight-loop case. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022033 |
[18] |
Maoan Han, Tonghua Zhang. Some bifurcation methods of finding limit cycles. Mathematical Biosciences & Engineering, 2006, 3 (1) : 67-77. doi: 10.3934/mbe.2006.3.67 |
[19] |
Fabio Scalco Dias, Luis Fernando Mello. The center--focus problem and small amplitude limit cycles in rigid systems. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1627-1637. doi: 10.3934/dcds.2012.32.1627 |
[20] |
J. C. Artés, Jaume Llibre, J. C. Medrado. Nonexistence of limit cycles for a class of structurally stable quadratic vector fields. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 259-270. doi: 10.3934/dcds.2007.17.259 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]