Results 81 to 90 of about 205,637 (167)

Bifurcation of a unique stable periodic orbit from a homoclinic orbit in infinite-dimensional systems

, 1989
Under some generic conditions, we show how a unique stable periodic orbit can bifurcate from a homoclinic orbit for semilinear parabolic equations and retarded functional differential equations.
Shui-Nee Chow, Bo Deng
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Existence of a homoclinic orbit in a generalized Liénard type system [PDF]

, 2021
The object of this paper is to study the existence and nonexistence of an important orbit in a generalized Liénard type system. This trajectory is doubly asymptotic to an equilibrium solution, i.e., an orbit which lies in the intersection of the stable ...
Kasbi Gharahasanlou Tohid, Roomi Vahid, Jodayree Akbarfam Aliasghar   +2 more
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Homoclinic orbits in 3D dissipative systems [PDF]

Scientific Technical Review, 2014
The paper deals with a variational system corresponding to a three-dimensional dynamic system. The characteristic equation of the variational system depends on partial solutions. The matrix of the right-hand part of the variational system is a sum of two
Martynyuk Andreevich Anatoly, Nikitina Vladimirovna Nelli   +1 more
doaj  

Homoclinic orbits for a class of $p$-Laplacian systems with periodic assumption

Electronic Journal of Qualitative Theory of Differential Equations, 2013
In this paper, by using a linking theorem, some new existence criteria of homoclinic orbits are obtained for the $p$-Laplacian system $d(|\dot{u}(t)|^{p-2}\dot{u}(t))/dt+\nabla V(t,x)=f(t)$, where $p>1$, $V(t,x)=-K(t,x)+W(t,x)$.
Xingyong Zhang
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Periodic or homoclinic orbit bifurcated from a heteroclinic loop for high-dimensional systems

Open Mathematics
Consider an autonomous ordinary differential equation in Rn{{\mathbb{R}}}^{n}, which has a heteroclinic loop. Assume that the heteroclinic loop consists of two degenerate heteroclinic orbits γ1{\gamma }_{1}, γ2{\gamma }_{2} and two saddle points with ...
Long Bin, Yang Yiying
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Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization. [PDF]

Proc Natl Acad Sci U S A, 2023
Pinsky T.
europepmc   +1 more source

Encryption of Color Images Based on Chaotic Attractors Generated by ODE Systems Containing Module Nonlinearities

Journal of Optimization, Differential Equations and Their Applications
The main objective of this work is to construct an algorithm for modeling chaotic attractors using special neural ODEs with antisymmetric matrices (antisymmetric neural ODEs) and modular power nonlinearities.
Vasiliy Ye. Belozyorov, Natalia A. Guk, Danylo I. Yehoshkin   +2 more
doaj   +1 more source

Precise Orbit Determination for ADEOS-II [PDF]

, 2006
We performed the precise orbit determination of ADEOS-II using single frequency GPS data and reviewed the results. JAXA precise orbit determination system is called “GUTS (Global and high accUracy Trajectory determination system)”.
Yamamoto, Y., Nakamura, S., Montenbruck, Oliver, Kudo, N.   +3 more
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Center Manifolds for Homoclinic Solutions

, 2000
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
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Strange attractor in the unfolding of an inclination-flip homoclinic orbit

, 1996
We study the unfolding of a smooth vector-fieldXon ℝ3having a homoclinic orbit to a hyperbolic equilibrium point with three real eigenvalues satisfying − λss< λs< 0 < λuWe say that Γ is an inclination-flip homoclinic orbit if the extended ...
Vincent Naudot
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