Results 71 to 80 of about 8,022 (205)
HOMOCLINIC ORBITS OF NONPERIODIC SUPERQUADRATIC HAMILTONIAN SYSTEM [PDF]
Taiwanese Journal of Mathematics, 2009 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 ...
Zhang, Jian, Tang, Xianhua, Zhang, Wen
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Parametrically Excited Nonlinear Two-Degree-of-Freedom Systems with Repeated Natural Frequencies
Shock and Vibration, 1995 The method of normal forms is used to study the nonlinear response of two-degree-of-freedom systems with repeated natural frequencies and cubic nonlinearity to a principal parametric excitation.
A. H. Nayfeh, C. Chin, D. T. Mook
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Pseudoholomorphic curves and multiplicity of homoclinic orbits [PDF]
Duke Mathematical Journal, 1995 The authors consider a Hamiltonian system of the form \[ \dot x = J(x) H'(t;x) \tag{1} \] on a compact, smooth Riemannian manifold \(M\). The function \(H : \mathbb{R} \times TM \to \mathbb{R}\) is smooth, 1-periodic in time and admits a point \(q_0 \in M\) such that \[ H(t; q_0, 0) = 0,\quad H'(t;q_0, 0) = 0, \] \[ H(t; q_0, p) \geq 0,\quad H(t;q,0) <
Cieliebak, Kai, Séré, Eric
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Closed geodesics and the first Betti number
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We prove that, on any closed manifold of dimension at least two with non‐zero first Betti number, a C∞$C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this existence result combining a theorem of Mañé together with the following new theorem of ...
Gonzalo Contreras, Marco Mazzucchelli
wiley +1 more source
Periodic and homoclinic orbits in a toy climate model [PDF]
Nonlinear Processes in Geophysics, 1994 A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet.
M. Toner, A. D. Kirwan, Jr.
doaj
Control optimization and homoclinic bifurcation of a prey–predator model with ratio-dependent
Advances in Difference Equations, 2019 In this paper, a predator–prey model with ratio-dependent and impulsive state feedback control is constructed, where the pest growth rate is related to an Allee effect. Firstly, the existence condition of the homoclinic cycle is obtained by analyzing the
Zhenzhen Shi +3 more
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Homoclinic orbits and chaos in a pair of parametrically-driven coupled nonlinear resonators
, 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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Protected Chaos in a Topological Lattice
Advanced Science, Volume 12, Issue 28, July 24, 2025.Topological and chaotic dynamics are often considered incompatible, with one expected to dominate or disrupt the other. This work reveals that topological localization can persist even under strong chaotic dynamics and, counter‐intuitively, protect chaotic behavior.
Haydar Sahin +6 more
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Homoclinic orbit solutions of a one Dimensional Wilson-Cowan type model
Electronic Journal of Differential Equations, 2008 We analyze a time independent integral equation defined on a spatially extended domain which arises in the modelling of neuronal networks. In this paper, the coupling function is oscillatory and the firing rate is a smooth "heaviside-like" function ...
Edward P. Krisner
doaj
Partial Hyperbolicity and Homoclinic Tangencies [PDF]
, 2011 We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic ...
Crovisier, Sylvain +2 more
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