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This paper describes a previously undocumented phenomenon in dynamical
systems theory; namely, the occurrence of heteroclinic cycles that are structurally
stable within the space of Cr vector fields...
Exponential Dichotomies and Homoclinic Orbits from Heteroclinic Cycles
Exponential Dichotomies Homoclinic Orbits Heteroclinic Cycle Melnikov Function
2013/1/30
In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies.We give a Melnikov!atype condition assuring the existence ofhomoclinic orbits form ...
Heteroclinic Orbits for a Discrete Pendulum Equation
heteroclinic solution critical point discrete pendulum equa-tion minimization arguments
2011/2/25
About twenty years ago, Rabinowitz showed firstly that there exist heteroclinic orbits of autonomous Hamiltonian system joining two equilibria. A special case of autonomous Hamiltonian system is the c...
Bifurcation of robust heteroclinic cycles in spherically invariant systems with $\ell =3,4$ mode interaction
robust heteroclinic cycles spherically invariant
2010/4/7
Bifurcation with spherical symmetry and mode interaction is known to produce robust heteroclinic cycles between axisymmetric steady-states. The case of mode interaction with representations of $\SO3$ ...
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for ...
Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition
reversible condition homoclinic orbit periodic orbit saddle-focus
2007/12/11
In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-ho...
Homoclinic (Heteroclinic) Orbit of Complex Dynamical System and
Spiral Structure
complex system homoclinic (heteroclinic) orbit spiral structure
2007/8/15
2005Vol.43No.4pp.601-603DOI:
Homoclinic (Heteroclinic) Orbit of Complex Dynamical System and
Spiral Structure
FU Zun-Tao, LIU Shi-Da, LIU Shi-Kuo,
LIANG Fu-Ming, and XIN Guo-Jun
...