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Some bifurcation methods of finding limit cycles
1. | Department of Mathematics, Shanghai Normal University, Shanghai 200234 |
2. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240 PR, China |
[1] |
Lijun Wei, Xiang Zhang. Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2803-2825. doi: 10.3934/dcds.2016.36.2803 |
[2] |
Valery A. Gaiko. The geometry of limit cycle bifurcations in polynomial dynamical systems. Conference Publications, 2011, 2011 (Special) : 447-456. doi: 10.3934/proc.2011.2011.447 |
[3] |
Jihua Yang, Liqin Zhao. Limit cycle bifurcations for piecewise smooth integrable differential systems. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2417-2425. doi: 10.3934/dcdsb.2017123 |
[4] |
Meilan Cai, Maoan Han. Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters. Communications on Pure and Applied Analysis, 2021, 20 (1) : 55-75. doi: 10.3934/cpaa.2020257 |
[5] |
Xiang-Ping Yan, Wan-Tong Li. Stability and Hopf bifurcations for a delayed diffusion system in population dynamics. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 367-399. doi: 10.3934/dcdsb.2012.17.367 |
[6] |
Jihua Yang, Erli Zhang, Mei Liu. Limit cycle bifurcations of a piecewise smooth Hamiltonian system with a generalized heteroclinic loop through a cusp. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2321-2336. doi: 10.3934/cpaa.2017114 |
[7] |
Huanhuan Tian, Maoan Han. Limit cycle bifurcations of piecewise smooth near-Hamiltonian systems with a switching curve. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5581-5599. doi: 10.3934/dcdsb.2020368 |
[8] |
Wenye Liu, Maoan Han. Limit cycle bifurcations of near-Hamiltonian systems with multiple switching curves and applications. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022053 |
[9] |
Yuan Chang, Yuzhen Bai. Limit cycle bifurcations by perturbing piecewise Hamiltonian systems with a nonregular switching line via multiple parameters. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022090 |
[10] |
John Guckenheimer, Hinke M. Osinga. The singular limit of a Hopf bifurcation. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2805-2823. doi: 10.3934/dcds.2012.32.2805 |
[11] |
C. R. Zhu, K. Q. Lan. Phase portraits, Hopf bifurcations and limit cycles of Leslie-Gower predator-prey systems with harvesting rates. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 289-306. doi: 10.3934/dcdsb.2010.14.289 |
[12] |
Niclas Kruff, Sebastian Walcher. Coordinate-independent criteria for Hopf bifurcations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1319-1340. doi: 10.3934/dcdss.2020075 |
[13] |
Gheorghe Tigan. Degenerate with respect to parameters fold-Hopf bifurcations. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2115-2140. doi: 10.3934/dcds.2017091 |
[14] |
Eleonora Catsigeras, Marcelo Cerminara, Heber Enrich. Simultaneous continuation of infinitely many sinks at homoclinic bifurcations. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 693-736. doi: 10.3934/dcds.2011.29.693 |
[15] |
Leonardo Mora. Homoclinic bifurcations, fat attractors and invariant curves. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1133-1148. doi: 10.3934/dcds.2003.9.1133 |
[16] |
Matteo Franca, Russell Johnson, Victor Muñoz-Villarragut. On the nonautonomous Hopf bifurcation problem. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1119-1148. doi: 10.3934/dcdss.2016045 |
[17] |
Anatoly Neishtadt. On stability loss delay for dynamical bifurcations. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 897-909. doi: 10.3934/dcdss.2009.2.897 |
[18] |
Thorsten Hüls. A model function for non-autonomous bifurcations of maps. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 351-363. doi: 10.3934/dcdsb.2007.7.351 |
[19] |
Jisun Lim, Seongwon Lee, Yangjin Kim. Hopf bifurcation in a model of TGF-$\beta$ in regulation of the Th 17 phenotype. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3575-3602. doi: 10.3934/dcdsb.2016111 |
[20] |
Jianhe Shen, Shuhui Chen, Kechang Lin. Study on the stability and bifurcations of limit cycles in higher-dimensional nonlinear autonomous systems. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 231-254. doi: 10.3934/dcdsb.2011.15.231 |
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