Results 91 to 100 of about 3,396,163 (214)
Homoclinic solutions for a class of second order non-autonomous systems
Electronic Journal of Differential Equations, 2009 This article concerns the existence of homoclinic solutions for the second order non-autonomous system $$ ddot q+A dot q-L(t)q+W_{q}(t,q)=0, $$ where $A$ is a skew-symmetric constant matrix, $L(t)$ is a symmetric positive definite matrix depending ...
Ziheng Zhang, Rong Yuan
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Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems [PDF]
, 2007 summary:We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The
Hiraoka, Yasuaki
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Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities [PDF]
, 2010 This paper continues an investigation into a one-dimensional lattice equation that models the light field in a system comprised of a periodic array of pumped optical cavities with saturable nonlinearity.
Champneys, AR, Yulin, AV
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, 2005 A new method for rigorously establishing the existence of a transversal homoclinic orbit to a periodic orbit (or a fixed point) of diffeomorphisms in Rn is presented. It is a computer-assisted technique with two main components.
Coomes, Brian +2 more
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Homoclinic bifurcations in a planar dynamical system
, 2022 S.1183-1191The homoclinic bifurcation properties of a planar dynamical system are analyzed and the corresponding bifurcation diagram is presented. The occurrence of two Bogdanov-Takens bifurcation points provides two local existing curves of homoclinic ...
Kuepper, T., Giannakopoulos, F., Zou, Y.
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, 2001 Cascades of period-doubling bifurcation,; have attracted much interest from researchers of dynamical systems in the past two decades as they are one of the routes to onset of chaos.
KOKUBU, Hiroshi +5 more
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Saddle-node bifurcations of multiple homoclinic solutions in ODES
Discrete and Continuous Dynamical Systems - B, 2017 The authors study periodic perturbations of differential equations possessing a homoclinic orbit along which the tangent spaces of the corresponding stable and unstable manifolds intersect in a three-dimensional space. This paper can be seen as a continuation of the work ``Multiple transverse homoclinic solutions near a degenerate homoclinic orbit ...
Lin, Xiao-Biao, Zhu, Changrong
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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 EquationsShilnikov'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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Homoclinic solutions of singular differential equations with $\phi$-Laplacian
Electronic Journal of Qualitative Theory of Differential Equations, 2018 A singular nonlinear initial value problem (IVP) with a $\phi$-Laplacian of the form $$ (p(t)\phi(u'(t)))'+ p(t)f(\phi(u(t)))=0, \quad u(0)=u_0 \in [L_0,0),\quad u'(0)=0 $$ is investigated on the half-line $[0,\infty)$.
Lukáš Rachůnek, Irena Rachůnková
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Advances in Difference Equations, 2017 In this paper, we investigate the existence and multiplicity of homoclinic solutions for a class of nonlinear difference systems involving classical ( ϕ 1 , ϕ 2 ) $(\phi_{1},\phi _{2})$ -Laplacian and a parameter: { Δ ( ρ 1 ( n − 1 ) ϕ 1 ( Δ u 1 ( n − 1 )
Xingyong Zhang +3 more
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