Results 111 to 120 of about 5,968 (173)
Resonant Homoclinic Flip Bifurcations
, 1998 This paper studies three-parameter unfoldings of resonant orbit flip and inclination flip homoclinic orbits. First all known results on codimension-two unfoldings of homoclinic flip bifurcations are presented.
Bernd Krauskopf, Ale Jan Homburg
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Newhouse phenomenon and homoclinic classes
, 2010 We show that for a C1 generic subset of diffeomorphisms far from homoclinic tangencies, any infinite sequence of sinks or sources must accumulate on a homoclinic class of some saddle point with codimension one.
JIAGANG YANG
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Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems
Abstract and Applied Analysis, 2012 We study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H∈C1(R×R2N,R) is the form H(t,z)=(1/2)B(t)z⋅z+R(t,z). We introduce a new assumption on B(t) and prove that the corresponding Hamiltonian operator has only point spectrum.
Wenping Qin, Jian Zhang, Fukun Zhao
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Resonant homoclinic flip bifurcations:a numerical investigation [PDF]
, 1999 We report on a numerical study of codimension-three resonant inclination flip homoclinic orbits. Two cases of unfoldings are presented: one with a single homoclinic doubling, and the other containing a homoclinic-doubling cascade. Our results confirm the
Oldeman, BE, Champneys, AR, Krauskopf, B
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Construction of codimension one homoclinic cycles
, 2014 We give an explicit construction of families of D-m-equivariant polynomial vector fields in R-4 possessing a codimension one homoclinic cycle. The homoclinic cycle consists of m homoclinic trajectories all connected to the equilibrium at the origin.
Homburg, A.J. +5 more
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MathematicsIn this paper, we investigate the multi-scale dynamics of a singularly perturbed Rosenzweig–MacArthur model with a generalist predator and identify dynamical phenomena, including equilibrium bifurcations, supercritical or subcritical singular Hopf ...
Xiao Wu, Shuaiwen Dan, Feng Xie
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Intersection of homoclinic classes on singular-hiperbolic sets
, 2010 Nosotros conocemos que dos clases homoclínicas diferentes contenidas en un conjunto hiperbólico son disjuntas. Además un conjunto transitivo singular-hiperbólico con orbitas periódicas densas y una única singularidad es transitivo o es unión de dos ...
Escobar Fiesco, Germán Fabian
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Homoclinic solutions for a class of second order non-autonomous systems
Electronic Journal of Differential Equations, 2009 This article concerns the existence of homoclinic solutions for the second order non-autonomous system $$ ddot q+A dot q-L(t)q+W_{q}(t,q)=0, $$ where $A$ is a skew-symmetric constant matrix, $L(t)$ is a symmetric positive definite matrix depending ...
Ziheng Zhang, Rong Yuan
doaj
, 2017 : Floer theory was originally devised to estimate the number of 1-periodic orbits of Hamiltonian systems. In earlier works, we constructed Floer homology for homoclinic orbits on two dimensional manifolds using combinatorial techniques.
Sonja Hohloch, Hohloch, Sonja
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Homoclinic Points Calculation Method With Particle Swarm Optimization
IEEE AccessThis paper proposes a novel algorithm to accurately calculate the coordinates of homoclinic points observed in discrete-time dynamical systems. The proposed method is based on the particle swarm optimization method. Compared with the current methods, the
Tatsumi Makino +3 more
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