An Index Theory with Applications to Homoclinic Orbits of Hamiltonian Systems and Dirac Equations
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DOI: 10.1007/s10884-020-09846-3
Abstract: In this paper, we will define the index pair $$(i_A(B),\nu _A(B))$$ ( i A ( B ) , ν A ( B ) ) by the dual variational method, and show the relationship between the… read more here.
Keywords: dirac equations; index; homoclinic orbits; index theory ... See more keywords
Fast homoclinic orbits for a class of damped vibration systems
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DOI: 10.1007/s11587-020-00534-4
Abstract: We study the existence of fast homoclinic orbits for the following damped vibration system $$\ddot{u}(t)+q(t)\dot{u}(t)+\nabla V(t,u(t))=0$$ ; where $$q\in C(\mathbb {R},\mathbb {R})$$ and $$V\in C^{1}(\mathbb {R}\times \mathbb {R}^{N},\mathbb {R})$$ is of the type V(t,x)=-K(t,x)+W(t,x). A… read more here.
Keywords: fast homoclinic; mathbb mathbb; homoclinic orbits; damped vibration ... See more keywords
Homoclinic orbits in the Euler problem of two fixed centers
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2018.05.026
Abstract: We give a complete description of the shapes and the behavior of all homoclinic orbits in the Euler problem of two fixed centers. read more here.
Keywords: two fixed; euler problem; homoclinic orbits; fixed centers ... See more keywords
On the existence of homoclinic orbits in n-dimensional piecewise affine systems
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DOI: 10.1016/j.nahs.2017.09.006
Abstract: Abstract Based on the mathematical analysis of the stable manifolds, unstable manifolds and solutions of subsystems, this paper provides methodologies to ensure the existence of homoclinic orbits (degenerate and non-degenerate) which cross the switching manifold… read more here.
Keywords: existence homoclinic; homoclinic orbits; affine systems; piecewise affine ... See more keywords
Numerical proof for chemostat chaos of Shilnikov's type.
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DOI: 10.1063/1.4977979
Abstract: A classical chemostat model is considered that models the cycling of one essential abiotic element or nutrient through a food chain of three trophic levels. The long-time behavior of the model was known to exhibit… read more here.
Keywords: proof chemostat; chemostat; homoclinic orbits; model ... See more keywords
Periodic motions and homoclinic orbits in a discontinuous dynamical system on a single domain with multiple vector fields.
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DOI: 10.1063/5.0085548
Abstract: In this paper, periodic motions and homoclinic orbits in a discontinuous dynamical system on a single domain with two vector fields are discussed. Constructing periodic motions and homoclinic orbits in discontinuous dynamical systems is very… read more here.
Keywords: homoclinic orbits; periodic motions; discontinuous dynamical; dynamical system ... See more keywords