Homoclinic and Heteroclinic Neural ODEs: Theory and Its Use to Construct New Chaotic Attractors
Journal of Optimization, Differential Equations and Their ApplicationsNew types of neural ordinary differential equations (NODE) with power nonlinearities are considered. For these NODE systems, new conditions for the existence of homoclinic and heteroclinic orbits are found.
Vasiliy Ye. Belozyorov +2 more
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Homoclinic orbits at infinity for second-order Hamiltonian systems with fixed energy
Electronic Journal of Differential Equations, 2015 We obtain the existence of homoclinic orbits at infinity for a class of second-order Hamiltonian systems with fixed energy. We use the limit for a sequence of approximate solutions which are obtained by variational methods.
Dong-Lun Wu, Shiqing Zhang
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Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries
Electronic Journal of Differential Equations, 1999 This paper deals via variational methods with the existence of infinitely many homoclinic orbits for a class of the first-order time-dependent Hamiltonian systems $$ dot{z}=JH_z(t,z) $$ without any periodicity assumption on $H$, providing that $H(t,z ...
Cheng Lee
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Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials
Abstract and Applied Analysis, 2009 This paper concerns solutions for the Hamiltonian system: z˙=𝒥Hz(t,z). Here H(t,z)=(1/2)z⋅Lz+W(t,z), L is a 2N×2N symmetric matrix, and W∈C1(ℝ×ℝ2N,ℝ).
Jian Ding, Junxiang Xu, Fubao Zhang
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Invariant manifolds of homoclinic orbits: super-homoclinics and multi-pulse homoclinic loops
, 2020 Consider a Hamiltonian flow on R4 with a hyperbolic equilibrium O and a transverse homoclinic orbit Γ. In this thesis, we study the dynamics near Γ in its energy level when it leaves and enters O along strong unstable and strong stable directions, respectively. In particular, we provide necessary and sufficient conditions for the existence of the local
openaire +2 more sources
Periodic and homoclinic orbits in a toy climate model [PDF]
Nonlinear Processes in Geophysics, 1994 A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet.
M. Toner, A. D. Kirwan, Jr.
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Solitary waves and homoclinic orbits [PDF]
, 1994 The notion that fluid motion often organizes itself into coherent structures has increasingly permeated modern fluid dynamics. Such localized objects appear in laminar flows and persist in turbulent states; from the water on windows on rainy days, to the circulations in planetary atmospheres. This review concerns solitary waves in fluids.
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Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization. [PDF]
Proc Natl Acad Sci U S A, 2023 Pinsky T.
europepmc +1 more source
Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system. [PDF]
Sci Rep, 2023 Wang H, Ke G, Pan J, Su Q.
europepmc +1 more source
Correction: An SIRS model with nonmonotone incidence and saturated treatment in a changing environment. [PDF]
J Math Biol, 2023 Pan Q, Huang J, Wang H.
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