Results 11 to 20 of about 3,396,163 (214)

Generalized homoclinic solutions for the Swift–Hohenberg equation [PDF]

Journal of Mathematical Analysis and Applications, 2012
The authors study the Swift-Hohenberg equation, which depends on one parameter and describes the onset of the Rayleigh-Bénard heat convection. By giving an explicit construction, they prove the existence of a homoclinic solution connecting a periodic orbit for every positive parameter.
Deng, Shengfu, Li, Xiaopei
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Homoclinic orbits for a class of symmetric Hamiltonian systems [PDF]

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
doaj   +3 more sources

The Existence of Transverse Homoclinic Solutions for Higher Order Equations [PDF]

Journal of Differential Equations, 1996
Parametrized differential equations of the form \(\dot x(t)=f(x(t),\mu,t)\), where \(x\in \mathbb{R}^n\), \(\mu\in \mathbb{R}^N\), are considered. It is assumed that \(f\) is of \(C^3\)-class, \(f(x,0,t)\) is independent of \(t\), for all sufficiently small \(|\mu|\), \(x=0\) is a hyperbolic equilibrium, \(f\) is periodic in \(t\), and there exists a ...
Gruendler, Joseph
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Multiple bursting patterns in lateral habenula neurons: Experiments and computational model. [PDF]

J Physiol
Abstract figure legend LHb neurons display a variety of bursting patterns, as well as being silent or displaying a tonic or irregular firing pattern. In a set of patch‐clamp experiments in ex vivo mouse lateral habenula (LHb), we were able to record from a number of cells showing characteristic bursts of a few distinguishable types.
Fedorov D, Campillo F, Desroches M, Soria-Gómez E, Rodrigues S, Piriz J.   +5 more
europepmc   +2 more sources

Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits [PDF]

, 2008
In this paper we consider the orbital previous termdynamicsnext term of a previous termsolar sailnext term in the Earth-Sun circular restricted three-body problem. The equations of motion of the previous termsailnext term are given by a set of non-linear
Waters, Thomas, McInnes, Colin, Waters, Thomas J., McInnes, Colin R.   +3 more
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Towards global models near homoclinic tangencies of dissipative diffeomorphisms [PDF]

, 1998
A representative model of a return map near homoclinic bifurcation is studied. This model is the so-called fattened Arnold map, a diffeomorphism of the annulus. The dynamics is extremely rich, involving periodicity, quasiperiodicity and chaos. The method
Broer, H; id_orcid, Simó, Carles,, Simo, C, Tatjer, JC, Broer, Henk,, Broer, H, Tatjer, Joan Carles,   +6 more
core   +2 more sources

Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point [PDF]

, 1994
Beyn W-J. Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point. IMA Journal of Numerical Analysis. 1994;14(3):381-410.It is known that branches of homoclinic orbits emanate from a singular point of a dynamical system with a ...
Beyn, Wolf-Jürgen
core   +1 more source

The numerical computation of connecting orbits in dynamical systems [PDF]

, 1990
Beyn W-J. The numerical computation of connecting orbits in dynamical systems. IMA Journal of Numerical Analysis. 1990;10(3):379-405.Structural changes in dynamical systems are often related to the appearance or disappearance of orbits connecting two ...
Beyn, Wolf-Jürgen
core   +1 more source

On Existence of Infinitely Many Homoclinic Solutions

Monatshefte f�r Mathematik, 2000
Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation ...
Wójcik, Klaudiusz, Zgliczyński, Piotr
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Homoclinic Solutions of Hamiltonian Systems with Symmetry

Journal of Differential Equations, 1999
Consider a Hamiltonian system with a Hamiltonian of the following form: \[ H(z,t)=\tfrac{1}{2}Az\cdot z+F(z,t). \] The authors show that if (i) the spectrum of the matrix \(JA\) (where \(J\) is the standard symplectic matrix) does not intersect the imaginary axis; (ii) \(F\) is invariant under the action of a compact Lie group; and (iii) \(F\) is ...
ARIOLI, GIANNI, A. Szulkin
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