Results 71 to 80 of about 481 (186)

Global bifurcation of a cubic system perturbed by degree four

上海师范大学学报. 自然科学版, 2014
Using the method of multi-parameter perturbation theory and qualitative analysis, a cubic system perturbed by degree four are investigated in this paper. After systematic analysis, it is found that the studied system can have nine limit cycles with their
Desheng Shang, Zheng Wang
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On Shilnikov's scenario in 3D: Topological chaos for vectorfields of class $C^1$

Electronic Journal of Qualitative Theory of Differential Equations
Shilnikov's scenario in $\mathbb{R}^3$ means that the equation $x'=V(x)\in\mathbb{R}^3$ with $V(0)=0$ has a homoclinic solution and the eigenvalues of $DV(0)$ are $u>0$ and $\sigma\pm i\mu$ with ...
Hans-Otto Walther
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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, Hale, Jack K., Mallet-Paret, John   +2 more
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Exploring the Influence of Oblateness on Asymptotic Orbits in the Hill Three-Body Problem

AppliedMath
We examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear ...
Vassilis S. Kalantonis
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Existence of homoclinic orbits for a class of nonlinear functional difference equations

Electronic Journal of Differential Equations, 2016
By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz ...
Xia Liu, Tao Zhou, Haiping Shi
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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 \(X=(x,y)\in\mathbb{C}\times\mathbb{C}^{n-1}\).
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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).
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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 ...
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Homoclinic orbits in 3D dissipative systems [PDF]

Scientific Technical Review, 2014
The paper deals with a variational system corresponding to a three-dimensional dynamic system. The characteristic equation of the variational system depends on partial solutions. The matrix of the right-hand part of the variational system is a sum of two
Martynyuk Andreevich Anatoly, Nikitina Vladimirovna Nelli   +1 more
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Homoclinic orbits for a class of $p$-Laplacian systems with periodic assumption

Electronic Journal of Qualitative Theory of Differential Equations, 2013
In this paper, by using a linking theorem, some new existence criteria of homoclinic orbits are obtained for the $p$-Laplacian system $d(|\dot{u}(t)|^{p-2}\dot{u}(t))/dt+\nabla V(t,x)=f(t)$, where $p>1$, $V(t,x)=-K(t,x)+W(t,x)$.
Xingyong Zhang
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