The point charge oscillator: qualitative and analytical investigations
Mathematical Modelling and Analysis, 2019 We study the mathematical model of the point charge oscillator which has been derived by A. Beléndez et al. [2]. First we determine the global phase portrait of this model in the Poincaré disk.
Klaus R. Schneider
doaj +1 more source
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
doaj +1 more source
Perturbed Li–Yorke homoclinic chaos
Electronic Journal of Qualitative Theory of Differential Equations, 2018 It is rigorously proved that a Li–Yorke chaotic perturbation of a system with a homoclinic orbit creates chaos along each periodic trajectory. The structure of the chaos is investigated, and the existence of infinitely many almost periodic orbits out of ...
Marat Akhmet +3 more
doaj +1 more source
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
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
doaj
Computation of Homoclinic Orbits in Partial Differential Equations: An Application to Cylindrical Shell Buckling [PDF]
, 1999 Gabriel J. Lord +2 more
openalex +1 more source
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
doaj
Multibreathers and homoclinic orbits in 1-dimensional nonlinear lattices [PDF]
, 2000 Tassos Bountis +5 more
openalex +1 more source
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 +1 more source
Gravity waves from homoclinic orbits of compact binaries [PDF]
, 2000 Janna Levin +2 more
openalex +1 more source