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Heteroclinic Orbits for a Discrete Pendulum Equation [PDF]
, 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.
Huafeng Xiao, Jianshe Yu
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Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics [PDF]
, 2000 In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem.
Wang Sang Koon +3 more
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Scarring by Homoclinic and Heteroclinic Orbits [PDF]
, 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 ...
Diego A. Wisniacki +3 more
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Periodic or homoclinic orbit bifurcated from a heteroclinic loop for high-dimensional systems
Open MathematicsConsider an autonomous ordinary differential equation in Rn{{\mathbb{R}}}^{n}, which has a heteroclinic loop. Assume that the heteroclinic loop consists of two degenerate heteroclinic orbits γ1{\gamma }_{1}, γ2{\gamma }_{2} and two saddle points with ...
Long Bin, Yang Yiying
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Dissipation-Induced Heteroclinic Orbits in Tippe Tops [PDF]
, 2008 This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex version of the equations for a simple harmonic oscillator ...
Nawaf Bou‐Rabee +2 more
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Globally Exponentially Attracting Sets and Heteroclinic Orbits Revealed [PDF]
MathematicsMotivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov ...
Guiyao Ke
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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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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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Global orbit of a complicated nonlinear system with the global dynamic frequency method
Journal of Low Frequency Noise, Vibration and Active Control, 2021 Global orbits connect the saddle points in an infinite period through the homoclinic and heteroclinic types of manifolds. Different from the periodic movement analysis, it requires special strategies to obtain expression of the orbit and detect the ...
Zhixia Wang +3 more
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Global Bifurcation Behaviors and Control in a Class of Bilateral MEMS Resonators
Fractal and Fractional, 2022 The investigation of global bifurcation behaviors the vibrating structures of micro-electromechanical systems (MEMS) has received substantial attention. This paper considers the vibrating system of a typical bilateral MEMS resonator containing fractional
Yijun Zhu, Huilin Shang
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