-
Previous Article
Threshold dynamics in a time-delayed periodic SIS epidemic model
- DCDS-B Home
- This Issue
-
Next Article
Global bifurcation for discrete competitive systems in the plane
Bifurcation analysis in models of tumor and immune system interactions
1. | Department of Mathematics, East China Normal University, Shanghai 200062, China |
2. | Department of Mathematics, The University of Miami, P.O. Box 249085, Coral Gables, Florida 33124 |
[1] |
Majid Gazor, Mojtaba Moazeni. Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 205-224. doi: 10.3934/dcds.2015.35.205 |
[2] |
Rui Dilão, András Volford. Excitability in a model with a saddle-node homoclinic bifurcation. Discrete and Continuous Dynamical Systems - B, 2004, 4 (2) : 419-434. doi: 10.3934/dcdsb.2004.4.419 |
[3] |
Ping Liu, Junping Shi, Yuwen Wang. A double saddle-node bifurcation theorem. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2923-2933. doi: 10.3934/cpaa.2013.12.2923 |
[4] |
Bing Zeng, Shengfu Deng, Pei Yu. Bogdanov-Takens bifurcation in predator-prey systems. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3253-3269. doi: 10.3934/dcdss.2020130 |
[5] |
Flaviano Battelli. Saddle-node bifurcation of homoclinic orbits in singular systems. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 203-218. doi: 10.3934/dcds.2001.7.203 |
[6] |
Jicai Huang, Sanhong Liu, Shigui Ruan, Xinan Zhang. Bogdanov-Takens bifurcation of codimension 3 in a predator-prey model with constant-yield predator harvesting. Communications on Pure and Applied Analysis, 2016, 15 (3) : 1041-1055. doi: 10.3934/cpaa.2016.15.1041 |
[7] |
Min Lu, Chuang Xiang, Jicai Huang. Bogdanov-Takens bifurcation in a SIRS epidemic model with a generalized nonmonotone incidence rate. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3125-3138. doi: 10.3934/dcdss.2020115 |
[8] |
Hebai Chen, Xingwu Chen, Jianhua Xie. Global phase portrait of a degenerate Bogdanov-Takens system with symmetry. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1273-1293. doi: 10.3934/dcdsb.2017062 |
[9] |
Hebai Chen, Xingwu Chen. Global phase portraits of a degenerate Bogdanov-Takens system with symmetry (Ⅱ). Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4141-4170. doi: 10.3934/dcdsb.2018130 |
[10] |
Xun Cao, Xianyong Chen, Weihua Jiang. Bogdanov-Takens bifurcation with $ Z_2 $ symmetry and spatiotemporal dynamics in diffusive Rosenzweig-MacArthur model involving nonlocal prey competition. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022031 |
[11] |
Victoriano Carmona, Soledad Fernández-García, Antonio E. Teruel. Saddle-node of limit cycles in planar piecewise linear systems and applications. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5275-5299. doi: 10.3934/dcds.2019215 |
[12] |
Ale Jan Homburg, Todd Young. Intermittency and Jakobson's theorem near saddle-node bifurcations. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 21-58. doi: 10.3934/dcds.2007.17.21 |
[13] |
W.-J. Beyn, Y.-K Zou. Discretizations of dynamical systems with a saddle-node homoclinic orbit. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 351-365. doi: 10.3934/dcds.1996.2.351 |
[14] |
Xiao-Biao Lin, Changrong Zhu. Saddle-node bifurcations of multiple homoclinic solutions in ODES. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1435-1460. doi: 10.3934/dcdsb.2017069 |
[15] |
Qiuyan Zhang, Lingling Liu, Weinian Zhang. Bogdanov-Takens bifurcations in the enzyme-catalyzed reaction comprising a branched network. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1499-1514. doi: 10.3934/mbe.2017078 |
[16] |
Amy H. Lin. A model of tumor and lymphocyte interactions. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 241-266. doi: 10.3934/dcdsb.2004.4.241 |
[17] |
Kie Van Ivanky Saputra, Lennaert van Veen, Gilles Reinout Willem Quispel. The saddle-node-transcritical bifurcation in a population model with constant rate harvesting. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 233-250. doi: 10.3934/dcdsb.2010.14.233 |
[18] |
Zhihua Liu, Rong Yuan. Takens–Bogdanov singularity for age structured models. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2041-2056. doi: 10.3934/dcdsb.2019201 |
[19] |
Fátima Drubi, Santiago Ibáñez, David Rivela. Chaotic behavior in the unfolding of Hopf-Bogdanov-Takens singularities. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 599-615. doi: 10.3934/dcdsb.2019256 |
[20] |
Eric Benoît. Bifurcation delay - the case of the sequence: Stable focus - unstable focus - unstable node. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 911-929. doi: 10.3934/dcdss.2009.2.911 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]