Results 81 to 90 of about 1,641 (211)
Homoclinic orbits in generalized Liénard systems
Journal of Mathematical Analysis and Applications, 2005 The author considers the planar Liénard-type system \[ \dot{x}=h(y)-F(x),\; \dot{y}=-g(x), \] where the functions \(F(x)\) and \(g(x)\) are continuous on an open interval \(I\) containing \(0\) and \(h(y)\) is continuous and strictly increasing on \(\mathbb{R}.\) Sufficient conditions are given, under which the system has a homoclinic orbit, i.e., a ...
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Homoclinic orbits of second-order nonlinear difference equations
Electronic Journal of Differential Equations, 2015 We establish existence criteria for homoclinic orbits of second-order nonlinear difference equations by using the critical point theory in combination with periodic approximations.
Haiping Shi, Xia Liu, Yuanbiao Zhang
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On periodic solutions in the non-dissipative Lorenz model: the role of the nonlinear feedback loop
Tellus: Series A, Dynamic Meteorology and Oceanography, 2018 In this study, we discuss the role of the linear heating term and nonlinear terms associated with a non-linear feedback loop in the energy cycle of the three-dimensional (X–Y–Z) non-dissipative Lorenz model (3D-NLM), where (X, Y, Z) represent the ...
B.-W. Shen
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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
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Bifurcation of a unique stable periodic orbit from a homoclinic orbit in infinite-dimensional systems [PDF]
, 1989 Shui-Nee Chow, Bo Deng
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Homoclinic orbits for a class of Hamiltonian systems
Differential and Integral Equations, 1992 The Hamiltonian system under consideration is governed by equations of the form \[ \ddot q+V_ q(t,q)=\ddot q-L(t)q+W_ q(t,q)=0, \] where \(L(t)\) is a positive definite matrix and further technical conditions, among other things, ensure that the origin is a local maximum of \(V\) for all \(t\).
Omana, W., Willem, M.
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Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition
Abstract and Applied Analysis, 2012 We study the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems q¨−L(t)q+∇qW(t,q)=0, where L(t) is unnecessarily positive definite for all t∈ℝ, and ∇qW(t,q) is of at most linear growth and satisfies some twist condition ...
Qi Wang, Qingye Zhang
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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
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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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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
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