Heteroclinic Orbits for a Discrete Pendulum Equation [PDF]
Journal of Difference Equations and Applications, 2010 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 classical pendulum equation.
Xiao, Huafeng, Yu, Jianshe
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Homoclinic and Heteroclinic Orbits in Climbing Cucumber Tendrils. [PDF]
Sci Rep, 2019 AbstractMany biomaterials utilize chiral growth to imitate biological functions. A prominent example can be found in growing cucumbers, which use tendrils as winding support for both fixation and climbing. A number of tendril-mimicking materials and artificial plant-like mechanical machines have been developed to imitate tendril deformation.
Feng J, Zhang W, Liu C, Guo M, Zhang C.
europepmc +5 more sources
Multitudinous potential homoclinic and heteroclinic orbits seized
Electronic Research ArchiveRevisiting a newly reported modified Chen system by both the definitions of $ \alpha $-limit and $ \omega $-limit set, Lyapunov function and Hamiltonian function, this paper seized a multitude of pairs of potential heteroclinic orbits to (1) $ E_{0 ...
Haijun Wang, Jun Pan, Guiyao Ke
doaj +3 more sources
Scarring by homoclinic and heteroclinic orbits [PDF]
Physical Review Letters, 2006 In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated ...
A. M. Ozorio de Almeida +7 more
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Persistence of the heteroclinic loop under periodic perturbation
Electronic Research Archive, 2023 We consider an autonomous ordinary differential equation that admits a heteroclinic loop. The unperturbed heteroclinic loop consists of two degenerate heteroclinic orbits $ \gamma_1 $ and $ \gamma_2 $.
Bin Long, Shanshan Xu
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Saddle-Node Heteroclinic Orbit and Exact Nontraveling Wave Solutions for (2+1)D KdV-Burgers Equation [PDF]
Abstract and Applied Analysis, 2013 We have undertaken the fact that the periodic solution of (2+1)D KdV-Burgers equation does not exist. The Saddle-node heteroclinic orbit has been obtained.
Da-Quan Xian
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A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations [PDF]
Journal of Mathematics, 2021 This work extends the high-order Melnikov method established by FJ Chen and QD Wang to heteroclinic orbits, and it is used to prove, under a certain class of perturbations, the heteroclinic orbit in a planar vector field that remains unbroken ...
Yi Zhong
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The heteroclinic orbit and tracking attractor in a cosmological model with a double exponential potential [PDF]
, 2005 In this paper, the dynamical heteroclinic orbit and attractor have been employed to make the late-time behaviour of the model insensitive to the initial condition and thus alleviating the fine-tuning problem in the cosmological dynamical system of a ...
Xin-zhou Li, Yi-bin Zhao, Chang-bo Sun
semanticscholar +3 more sources
Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria
The Scientific World Journal, 2014 The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Fengjie Geng, Junfang Zhao
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Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits [PDF]
AstrodynamicsHeteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic ΔV expenditure.
Danny Owen, Nicola Baresi
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