Results 51 to 60 of about 467 (169)
An example of bifurcation to homoclinic orbits
Journal of Differential Equations, 1980 AbstractConsider the equation ẍ − x + x2 = −λ1x + λ2ƒ(t) where ƒ(t + 1) = ƒ(t) and λ = (λ1, λ2) is small. For λ = 0, there is a homoclinic orbit Γ through zero. For λ ≠ 0 and small, there can be “strange” attractors near Γ. The purpose of this paper is to determine the curves in λ-space of bifurcation to “strange” attractors and to relate this to ...
Chow, Shui-Nee +2 more
openaire +2 more sources
BERNULLI DIFFERENTIAL EQUATION AND CHAOS
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2013 Existence conditions of homoclinic orbits for some systems of ordinary quadratic differential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic ...
V. Ye. Belozerov
doaj +1 more source
Existence of homoclinic orbits for unbounded time-dependent $p$-Laplacian systems
Electronic Journal of Qualitative Theory of Differential Equations, 2016 In this paper, we consider the following ordinary $p$-Laplacian system \begin{equation} \frac{d}{dt}\big(|\dot u(t)|^{p-2}\dot u(t)\big)-\nabla K(t,u(t)) + \nabla W(t,u(t))=f(t),\tag{$HS$} \end{equation} where $t\in \mathbb{R}$ and $ p>1$.
Adel Daouas
doaj +1 more source
A Note on the Existence of a Smale Horseshoe in the Planar Circular Restricted Three-Body Problem
Abstract and Applied Analysis, 2015 It has been proved that, in the classical planar circular restricted three-body problem, the degenerate saddle point processes transverse homoclinic orbits.
Xuhua Cheng, Zhikun She
doaj +1 more source
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 Orbits in Families of Hypersurfaces with Hyperbolic Periodic Orbits
Journal of Differential Equations, 2002 The author considers the Hamiltonian system \(\dot{X}=J\nabla H(X)\) on \(\mathbb{C}^n\) with a \(C^2\)-Hamiltonian \(H:\mathbb{C}^n\to\mathbb{R}\). Here \(J\) induces the standard symplectic structure on \(\mathbb{C}^n\). Denote \(X=(x,y)\in\mathbb{C}\times\mathbb{C}^{n-1}\).
openaire +2 more sources
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
Bifurcations of homoclinic orbits in bimodal maps
Physical Review E, 1994 We discuss the bifurcation structure of homoclinic orbits in bimodal one dimensional maps. The universal structure of these bifurcations with singular bifurcation points and the web of bifurcation lines through the parameter space are described. The bifurcations depend on two parameters (codimension 2 bifurcations).
openaire +3 more sources
Author’s reply to: Comments on “Asymptotically stable equilibrium points in new chaotic systems”
Nova Scientia, 2017 Since theorem 1 of (Elhadj and Sprott, 2012) is incorrect, some of the systems found in the article (Casas-García et al. 2016) may have homoclinic or heteroclinic orbits and may seem chaos in the Shilnikov sense.
K. Casas-García +4 more
doaj +1 more source
Homoclinic Orbits and Lagrangian Embeddings [PDF]
International Mathematics Research Notices, 2010 12 pages; fixed an error, provided more details, reorganized exposition of proof of Theorem 1 ...
openaire +2 more sources