Results 91 to 100 of about 8,022 (205)

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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A Numerical Bifurcation Function for Homoclinic Orbits

SIAM Journal on Numerical Analysis, 1998
Summary: The authors present a numerical method to locate periodic orbits near homoclinic orbits. Using a method of [\textit{X.-B. Lin}, Proc. R. Soc. Edinb., Ser. A 116, 295-325 (1990; Zbl 0714.34070)] and solutions of the adjoint variational equation, one gets a bifurcation function for periodic orbits, whose periods are asymptotic to infinity on ...
Ashwin, Peter, Mei, Zhen
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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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Numerical Algorithms for Homoclinic Orbits

, 2009
Dynamical systems occur in many areas of science, especially fluid dynamics. One is often interested in examining the structural changes in dynamical systems, and these are often related to the appearance or disappearance of solution trajectories connecting one or more stationary points.
Girdlestone, Stephen, Girdlestone, Stephen   +1 more
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Structurally Stable Homoclinic Classes [PDF]

, 2014
In this paper we study structurally stable homoclinic classes. In a natural way, the structural stability for an individual homoclinic class is defined through the continuation of periodic points.
Wen, Xiao
core  

Homoclinic Orbits for Asymptotically Linear Hamiltonian Systems

Journal of Functional Analysis, 2001
The existence of a homoclinic orbit is proved in the paper for a Hamiltonian system \[ \dot z=JH_z(z,t),\tag{1} \] where \(z=(p,q)\in \mathbb R^{2N}\) and \(J=\left (\begin{smallmatrix} 0 & -I\\ I & 0\end{smallmatrix} \right)\). Furthermore, \(H(z,t)=\frac{1}{2}Az\cdot z+G(z,t)\) and \(H(0,t)=0\) with \(G_z(z,t)/|z|\to 0\) uniformly in \(t\) as \(z\to ...
Szulkin, Andrzej, Zou, Wenming
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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 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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