논문KCI 등재
Persistence of homoclinic orbits after discretization of a two dimensional degenerate differential system
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
The aim of this work is to construct a general family of two dimensional differential systems which admits homoclinic solutions near a non-hyperbolic fixed point, such that a Jacobian matrix at this point is zero. We then discretize it by using Euler's method and look after the persistence of the homoclinic solutions in the obtained discrete system.
Abstract
The aim of this work is to construct a general family of two dimensional differential systems which admits homoclinic solutions near a non-hyperbolic fixed point, such that a Jacobian matrix at this point is zero. We then discretize it by using Euler's method and look after the persistence of the homoclinic solutions in the obtained discrete system.
참고문헌 (14)
- A. A. Andronov, "Qualitative Theory of Second Order Dynamic Systems" (1973), John Wiley and Sons
- W. J. Beyn, "The eect of discretization on homoclinic orbits, Bifurcation, Analysis, Algorithms, Applications", 1~8 (1987)
- W. J. Beyn, "On invariant closed curves for one-step methods", Numer. Math, 51(1), pp.103~122 (1987)
- W. J. Beyn, "Estimates of variable stepsize Runge-Kutta methods for sectorial evolution equations with nonsmooth data", Appl. Numer. Math, 41(3), pp.369~400 (2002)
- W. J. Beyn, "The numerical computation of homoclinic orbits for maps", SIAM J. Numer. Anal, 34(3), pp.1207~1236 (1997)
- W. J. Beyn, "A direct approach to homoclinic orbits in the fast dynamics of singularly perturbed systems", J. Dynam. Dierential Equations, 11(4), pp.671~709 (1999)
- N. Chen, "Visualizing the complex dynamics of families of polynomials with symmetric critical points", Chaos Solitons Fractals, 42(3), pp.1611~1622 (2009)
- E. J. Doedel, "Successive continuation for locating connecting orbits", Numer. Algorithms, 14(1-3), pp.103~124 (1997)
- E. J. Doedel, "On locating connecting orbits", Appl. Math. Comput, 65(1-3), pp.231~239 (1994)
- B. Fiedler, "Discretization of homoclinic orbits, rapid forcing and \invis-ible" chaos", Mem. Amer. Math. Soc, 119(570), pp.79~ (1996)
- S. J. Green eld, "Dynamics of a quadratic map in two complex variables", J. Dierential Equations, 169(1), pp.57~141 (2001)
- S. Lefschetz, "Dierential Equations: Geometric Theory" (1957), Interscience publishers
- N. Mehidi, "Homoclinic solutions in a quadratic di erential system under discretization", J. Dierence Equ. Appl, 19(4), pp.538~542 (2013)
- Y. K. Zou, "On manifolds of connecting orbits in discretizations of dynamical systems", Nonlinear Anal, 52(5), pp.1499~1520 (2003)
관련 논문AI추천
Persistence of Periodic Trajectories of Planar Systems under two Parametric PerturbationsOmid RabieiMotlagh, Zahra Afsharnejad대한수학회 · 대한수학회지2007 · 제44권 제3호EXISTENCE OF HOMOCLINIC ORBITS FOR LI¶ENARD TYPE SYSTEMS김용인한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제4호ON C1-GENERIC HYPERBOLICITY OF HOMOCLINIC CLASSES강보원, 이만섭, N. Koo장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제3호EXISTENCE OF PERIODIC SOLUTIONS FOR PLANAR HAMILTONIAN SYSTEMS AT RESONANCE김용인대한수학회 · 대한수학회지2011 · 제48권 제6호h-STABILITY OF PERTURBED DIFFERENTIAL SYSTEMS구윤회한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제4호h¡STABILITY OF NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t1-SIMILARITY구윤회, 양승범한국수학교육학회 · 이론수학과 교직수학2012 · 제19권 제2호
이 간행물의 다른 논문 (23건)
Global weak Morrey estimates for some Ultraparabolic operators of Kolmogorov-Fokker-Planck typeMaochun Zhu, Xiaojing Feng, Pengcheng Niupp. 1241-1257Hyperbolicity of chain transitive sets with limit shadowing이승희, Khosro Tajbakhsh, Abbas Fakharipp. 1259-1267Structural stability results for the thermoelasticity of type IIIYan Liupp. 1269-1279On the transcendental entire solutions of a class of differential equationsChungchun Yang, Weiran Lu, Qiuying Lipp. 1281-1289Value distribution of difference operator on meromorphic functionsLian-Zhong Yang, Jie Dingpp. 1291-1297