The existence of homoclinic orbits in the Lorenz system via the undetermined coefficient method
type: Item
instance of: scholarly article
title: The existence of homoclinic orbits in the Lorenz system via the undetermined coefficient method
zbMATH Open document ID: 1428.34062
author: Juan Song
author: Yanmin Niu
author: Xiong Li
published in: Applied Mathematics and Computation
publication date: 2019-11-28T00:00:00Z
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7138505
zbMATH Keywords: Lorenz system
zbMATH Keywords: homoclinic orbits
zbMATH Keywords: undetermined coefficient method
MaRDI profile type: Publication
full work available at URL: j.amc.2019.03.011
OpenAlex ID: W2925206705
cites work: A new method to find homoclinic and heteroclinic orbits
cites work: Q3697395
cites work: Šil'nikov homoclinic orbits in two classes of 3D autonomous nonlinear systems
cites work: Lorenz Equations Part I: Existence and Nonexistence of Homoclinic Orbits
cites work: Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems
cites work: Existence of a Homoclinic Orbit of the Lorenz System by Precise Shooting
cites work: A proof that the Lorenz equations have a homoclinic orbit
cites work: The Lorenz System: II. The Homoclinic Convolution of the Stable Manifolds
cites work: Q3202465
cites work: General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems
cites work: Shilnikov chaos in Lorenz-like systems
cites work: Fishing principle for homoclinic and heteroclinic trajectories
cites work: Necessary and sufficient conditions of the existence of homoclinic trajectories and cascade of bifurcations in Lorenz-like systems: birth of strange attractor and 9 homoclinic bifurcations
cites work: Lower bounds for the Hausdorff dimension of the geometric Lorenz attractor: The homoclinic case
cites work: Hopf bifurcation analysis in a Lorenz-type system
cites work: New Treatment on Bifurcations of Periodic Solutions and Homoclinic Orbits at High r in the Lorenz Equations
cites work: Deterministic Nonperiodic Flow
cites work: Chaos in the Lorenz equations: a computer-assisted proof
cites work: Nonsymmetric Lorenz Attractors from a Homoclinic Bifurcation
cites work: Convergence to equilibria in the Lorenz system via monotone methods
cites work: The Lorenz equations: bifurcations, chaos, and strange attractors
cites work: On the strange attractor and transverse homoclinic orbits for the Lorenz equations
cites work: Bounds for trajectories of the Lorenz equations: An illustration of how to choose Liapunov functions
cites work: Analytic approximation of the homoclinic orbits of the Lorenz system at \(\sigma=10\), \(b=8/3\) and \(\rho=13. 926\dots\)
cites work: Symbolic dynamics and periodic orbits of the Lorenz attractor*
cites work: Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system
Wikidata QID: Q128184545
DOI: 10.1016/J.AMC.2019.03.011
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description: scientific article; zbMATH DE number 7138505