Results 91 to 100 of about 16,375 (207)
Моделирование и анализ информационных систем, 2015 We consider a finite-dimensional model of phase oscillators with inertia in the case of star configuration of coupling. The system of equations is reduced to a nonlinearly coupled system of pendulum equations.
V. N. Belykh +2 more
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The Generalized Homoclinic Bifurcation
Journal of Differential Equations, 1994 The author considers a family \(X_ \lambda\) of vector fields that has at \(\lambda= 0\) a homoclinic loop of multiplicity \(n\). The aim of the paper is to present conditions of the versality of \(X\) in a neighborhood of the loop. For this, the author uses the representation of the displacement function given by \textit{R. Roussarie} [Bol. Soc. Bras.
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On the so called rogue waves in nonlinear Schrodinger equations
Electronic Journal of Differential Equations, 2016 The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial
Y. Charles Li
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, 2010 We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (it has
Crovisier, Sylvain, Pujals, Enrique R.
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Homoclinic orbits for a class of symmetric Hamiltonian systems
Electronic Journal of Differential Equations, 1994 of Hamiltonian systems that are symmetric with respect to independent variable (time). For the scalar case we prove existence and uniqueness of a positive homoclinic solution. For the system case we prove existence of symmetric homoclinic orbits.
Philip Korman, Alan C. Lazer
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Homoclinic intersections of symplectic partially hyperbolic systems with 2D center
, 2015 We study some generic properties of partially hyperbolic symplectic systems with 2D center. We prove that $C^r$ generically, every hyperbolic periodic point has a transverse homoclinic intersection for the maps close to a direct/skew product of an Anosov
Zhang, Pengfei
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Electronic Journal of Differential Equations, 2010 This article studies the existence of homoclinic solutions for the second-order non-autonomous Hamiltonian system $$ ddot q-L(t)q+W_{q}(t,q)=0, $$ where $Lin C(mathbb{R},mathbb{R}^{n^2})$ is a symmetric and positive definite matrix for all $tin ...
Rong Yuan, Ziheng Zhang
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Chaos Theory and ApplicationsThis paper presents the study of the opposition to the synchronization of bistable chaotic oscillator systems in basic motif configurations. The following configurations were analyzed: Driver-response oscillator systems coupling, two driver oscillator ...
Dıdıer Lopez Mancılla +3 more
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Homoclinic solutions for a class of non-periodic second order Hamiltonian systems
Electronic Journal of Qualitative Theory of Differential Equations, 2010 We study the existence of homoclinic solutions for the second order Hamiltonian system $\ddot{u}+V_{u}(t,u)=f(t)$. Let $V(t,u)=-K(t,u)+W(t,u)\in C^{1}(\mathbb{R}\times\mathbb{R}^{n}, \mathbb{R})$ be $T$-periodic in $t$, where $K$ is a quadratic growth ...
Jian Ding, Junxiang Xu, Fubao Zhang
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Bifurcation of homoclinics [PDF]
Proceedings of the American Mathematical Society, 2007 We show that homoclinic trajectories of nonautonomous vector fields parametrized by a circle bifurcate from the stationary solution when the asymptotic stable bundles of the linearization at plus and minus infinity are “twisted” in different ways.
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