NUMERICAL COMPUTATION OF SADDLE-NODE HOMOCLINIC BIFURCATION POINTS

被引：21
|
作者：
SCHECTER, S
机构：
[1] North Carolina State Univ, Raleigh, NC
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 1993年 / 30卷 / 04期
关键词：
SADDLE-NODE HOMOCLINIC BIFURCATION; CONVERGENCE; STABILITY; BOUNDARY-VALUE PROBLEM; MELNIKOV INTEGRAL; VARIATIONAL EQUATION;
D O I：
10.1137/0730060
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In two-parameter families of vector fields there can be curves in the parameter plane along which orbits homoclinic to hyperbolic equilibria occur. Such curves can end at a point where there is an orbit homoclinic to an equilibrium undergoing saddle-node or transcritical bifurcation. Convergence and stability results are presented for a method of approximating these special parameter values and their associated homoclinic orbits.
引用
收藏
页码：1155 / 1178
页数：24
相关论文
共 50 条
  • [21] Saddle-Node Bifurcation Leading to Survival Mosquitoes
    Franco-Perez, L.
    Nunez-Lopez, M.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2025, 35 (04):
  • [22] Numerical study of saddle-node bifurcation for longitudinal flight with CFD/RBD technique
    Chen Qi
    Yuan Xianxu
    Wang Xinguang
    Chen Jianqiang
    Xie Yufei
    JOURNAL OF COMPUTATIONAL SCIENCE, 2018, 29 : 153 - 162
  • [23] A non-transverse homoclinic orbit to a saddle-node equilibrium
    Champneys, AR
    Harterich, J
    Sandstede, B
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1996, 16 : 431 - 450
  • [24] On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node
    Gonchenko, Serey V.
    Gordeeva, Olga V.
    Lukyanov, Valery I.
    Ovsyannikov, Ivan I.
    REGULAR & CHAOTIC DYNAMICS, 2014, 19 (04): : 461 - 473
  • [25] On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node
    Serey V. Gonchenko
    Olga V. Gordeeva
    Valery I. Lukyanov
    Ivan I. Ovsyannikov
    Regular and Chaotic Dynamics, 2014, 19 : 461 - 473
  • [26] BREAKING OF SYMMETRY IN THE SADDLE-NODE HOPF-BIFURCATION
    KIRK, V
    PHYSICS LETTERS A, 1991, 154 (5-6) : 243 - 248
  • [27] BASIN ORGANIZATION PRIOR TO A TANGLED SADDLE-NODE BIFURCATION
    Soliman, Mohamed S.
    Thompson, J. M. T.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1991, 1 (01): : 107 - 118
  • [28] NONAUTONOMOUS SADDLE-NODE BIFURCATION IN A CANONICAL ELECTROSTATIC MEMS
    Gutierrez, Alexander
    Torres, Pedro J.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (05):
  • [29] Asymptotics of the Solution of a Differential Equation in a Saddle-Node Bifurcation
    Kalyakin, L. A.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2019, 59 (09) : 1454 - 1469
  • [30] QUASI-TRANSVERSAL SADDLE-NODE BIFURCATION ON SURFACES
    BELOQUI, J
    PACIFICO, MJ
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1990, 10 : 63 - 88
12345