Results 1 to 10 of about 10,505 (232)
Homoclinic Orbits in Several Classes of Three-Dimensional Piecewise Affine Systems with Two Switching Planes [PDF]
Mathematics, 2021 The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine ...
Yanli Chen, Lei Wang, Xiaosong Yang
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Homoclinic orbits of sub-linear Hamiltonian systems with perturbed terms [PDF]
Boundary Value Problems, 2021 By using variational methods, we obtain the existence of homoclinic orbits for perturbed Hamiltonian systems with sub-linear terms. To the best of our knowledge, there is no published result focusing on the perturbed and sub-linear Hamiltonian systems.
Haiyan Lv, Guanwei Chen
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Homoclinic Orbits In Slowly Varying Oscillators [PDF]
SIAM Journal on Mathematical Analysis, 1987 We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time.
Holmes, Philip, Wiggins, Stephen
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Scarring by homoclinic and heteroclinic orbits [PDF]
Physical Review Letters, 2006 In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated ...
A. M. Ozorio de Almeida +7 more
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Shil'nikov Chaos control using Homoclinic orbits and the Newhouse region [PDF]
, 2006 A method of controlling Shil'nikov's type chaos using windows that appear in the 1 dimensional bifurcation diagram when perturbations are applied, and using existence of stable homoclinic orbits near the unstable one is presented and applied to the ...
Furui, Sadataka, Niiya, Shohei
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Homoclinic orbits and chaos in a pair of parametrically-driven coupled nonlinear resonators [PDF]
, 2010 We study the dynamics of a pair of parametrically-driven coupled nonlinear mechanical resonators of the kind that is typically encountered in applications involving microelectromechanical and nanoelectromechanical systems (MEMS & NEMS). We take advantage
A. Cleland +7 more
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Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential [PDF]
Abstract and Applied Analysis, 2013 We investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with local superquadratic potential by using the Mountain Pass Theorem and the Fountain Theorem, respectively.
Ying Lv, Chun-Lei Tang
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Bifurcations of homoclinic orbits in bimodal maps [PDF]
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).
Kai T. Hansen
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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.
Stephen Girdlestone
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HOMOCLINIC ORBITS OF NONPERIODIC SUPERQUADRATIC HAMILTONIAN SYSTEM [PDF]
Taiwanese Journal of Mathematics, 2013 The authors consider the Hamiltonian system \[ \dot{u} = JH_u(t,u) \] where \[ H(t,u) = {{1}\over{2}}u^*Lu + W(t,u) \] and \(L\) is symmetric constant and \(W(t,u)\) is subject to some technical assumptions connected to super quadratic character. The main result of the paper is that under the assumptions mentioned above the system has at least one ...
Jian Zhang, Xianhua Tang, Wen Zhang
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