Results 21 to 30 of about 7,158,567 (167)

Existence and stability of multiple spot solutions for the Gray-Scott model in R^2$ [PDF]

, 2003
Existence and Stability of Multiple Spot Solutions for the Gray-Scott Model in $R^2$ In this paper, we rigorously prove the existence and stability of multiple spot patterns for the Gray-Scott system in a two dimensional domain which are far from ...
Wei, J
core   +1 more source

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

Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials [PDF]

Abstract and Applied Analysis, 2012
A class of difference equations which include discrete nonlinear Schrödinger equations as special cases are considered. New sufficient conditions of the existence and multiplicity results of homoclinic solutions for the difference equations are obtained by making use of the mountain pass theorem and the fountain theorem, respectively.
Ma, Defang, Zhou, Zhan
openaire   +3 more sources

Saddle-node bifurcations of multiple homoclinic solutions in ODES

Discrete and Continuous Dynamical Systems - B, 2017
The authors study periodic perturbations of differential equations possessing a homoclinic orbit along which the tangent spaces of the corresponding stable and unstable manifolds intersect in a three-dimensional space. This paper can be seen as a continuation of the work ``Multiple transverse homoclinic solutions near a degenerate homoclinic orbit ...
Lin, Xiao-Biao, Zhu, Changrong
openaire   +1 more source

Homoclinic orbits for a class of second-order Hamiltonian systems with concave-convex nonlinearities

Electronic Journal of Qualitative Theory of Differential Equations, 2018
In this paper, we study the existence of multiple homoclinic solutions for the following second order Hamiltonian systems \begin{equation*} \ddot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0, \end{equation*} where $L(t)$ satisfies a boundedness assumption which is ...
Dong-Lun Wu, Chun-Lei Tang, Xing-Ping Wu
doaj   +1 more source

Multiple homoclinic solutions for singular differential equations

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010
The homoclinic bifurcations of ordinary differential equation under singular perturbations are considered. We use exponential dichotomy, Fredholm alternative and scales of Banach spaces to obtain various bifurcation manifolds with finite codimension in an appropriate infinite-dimensional space. When the perturbative term is taken from these bifurcation
Zhu, Changrong, Luo, Guangping, Lan, Kunquan   +2 more
openaire   +1 more source

Center Manifolds for Homoclinic Solutions [PDF]

, 1995
In this article, center-manifold theory is developed for homoclinic solutions of ordinary differential equations or semilinear parabolic equations. A center manifold along a homoclinic solution is a locally invariant manifold containing all solutions ...
Sandstede, Björn, Björn Sandstede
core   +2 more sources

CODIAGONALIZATION OF MATRICES AND EXISTENCE OF MULTIPLE HOMOCLINIC SOLUTIONS

Journal of Applied Analysis & Computation, 2017
The purpose of this paper is twofold. First, we use Lagrange's method and the generalized eigenvalue problem to study systems of two quadratic equations. We find exact conditions so the system can be codiagonalized and can have up to 4 solutions. Second, we use this result to study homoclinic bifurcations for a periodically perturbed system.
null Xiaobiao Lin, null Changrong Zhu
openaire   +1 more source

Existence and stability of multiple spot solutions for the gray-scott model in R^2 [PDF]

, 2005
We study the Gray-Scott model in a bounded two dimensional domain and establish the existence and stability of {\bf symmetric} and {\bf asymmetric} multiple spotty patterns. The Green's function and its derivatives together with two nonlocal eigenvalue
Winter, M, Wei, J, JUNCHENG WEI, MATTHIAS WINTER   +3 more
core   +1 more source

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