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Discretizations of dynamical systems with a saddle-node homoclinic orbit
1. | Fakultät Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany |
2. | Department of Mathematics, Jilin University, Changchun 130023, China |
[1] |
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 |
[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] |
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 |
[4] |
Flaviano Battelli, Ken Palmer. A remark about Sil'nikov saddle-focus homoclinic orbits. Communications on Pure and Applied Analysis, 2011, 10 (3) : 817-830. doi: 10.3934/cpaa.2011.10.817 |
[5] |
Qinqin Zhang. Homoclinic orbits for discrete Hamiltonian systems with indefinite linear part. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1929-1940. doi: 10.3934/cpaa.2015.14.1929 |
[6] |
Chen-Chang Peng, Kuan-Ju Chen. Existence of transversal homoclinic orbits in higher dimensional discrete dynamical systems. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1181-1197. doi: 10.3934/dcdsb.2010.14.1181 |
[7] |
Qinqin Zhang. Homoclinic orbits for discrete Hamiltonian systems with local super-quadratic conditions. Communications on Pure and Applied Analysis, 2019, 18 (1) : 425-434. doi: 10.3934/cpaa.2019021 |
[8] |
Andrew J. Steyer, Erik S. Van Vleck. Underlying one-step methods and nonautonomous stability of general linear methods. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2859-2877. doi: 10.3934/dcdsb.2018108 |
[9] |
Ting Yang. Homoclinic orbits and chaos in the generalized Lorenz system. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 1097-1108. doi: 10.3934/dcdsb.2019210 |
[10] |
Ying Lv, Yan-Fang Xue, Chun-Lei Tang. Homoclinic orbits for a class of asymptotically quadratic Hamiltonian systems. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2855-2878. doi: 10.3934/cpaa.2019128 |
[11] |
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 |
[12] |
Quan Zhou, Yabing Sun. High order one-step methods for backward stochastic differential equations via Itô-Taylor expansion. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021233 |
[13] |
Addolorata Salvatore. Multiple homoclinic orbits for a class of second order perturbed Hamiltonian systems. Conference Publications, 2003, 2003 (Special) : 778-787. doi: 10.3934/proc.2003.2003.778 |
[14] |
Jianquan Li, Yanni Xiao, Yali Yang. Global analysis of a simple parasite-host model with homoclinic orbits. Mathematical Biosciences & Engineering, 2012, 9 (4) : 767-784. doi: 10.3934/mbe.2012.9.767 |
[15] |
Yingxiang Xu, Yongkui Zou. Preservation of homoclinic orbits under discretization of delay differential equations. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 275-299. doi: 10.3934/dcds.2011.31.275 |
[16] |
John Guckenheimer, Christian Kuehn. Homoclinic orbits of the FitzHugh-Nagumo equation: The singular-limit. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 851-872. doi: 10.3934/dcdss.2009.2.851 |
[17] |
Christian Bonatti, Lorenzo J. Díaz, Todd Fisher. Super-exponential growth of the number of periodic orbits inside homoclinic classes. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 589-604. doi: 10.3934/dcds.2008.20.589 |
[18] |
W.R. Derrick, P. van den Driessche. Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population. Discrete and Continuous Dynamical Systems - B, 2003, 3 (2) : 299-309. doi: 10.3934/dcdsb.2003.3.299 |
[19] |
Juntao Sun, Jifeng Chu, Zhaosheng Feng. Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3807-3824. doi: 10.3934/dcds.2013.33.3807 |
[20] |
Boris Buffoni, Laurent Landry. Multiplicity of homoclinic orbits in quasi-linear autonomous Lagrangian systems. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 75-116. doi: 10.3934/dcds.2010.27.75 |
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