Results 141 to 150 of about 467 (169)

CONSTRUCTING HOMOCLINIC ORBITS AND CHAOTIC ATTRACTORS

International Journal of Bifurcation and Chaos, 1994
Homoclinic orbits and chaotic attractors are constructed progressively by singular perturbations. More specifically, lower dimensional slow subsystems and fast subsystems are constructed separately as building blocks. The former are then modulated onto the latter via homotopy.
openaire   +2 more sources

Homoclinic/heteroclinic recurrent orbits and horseshoe

Journal of Differential Equations
In this paper, the authors consider systems of ODEs \[ \dot z = g(z) + \mu h(t,z,\mu) \] with a small parameter \(\mu \in \mathbb{R}\). Assuming that for \(\mu=0\) the system has a solution \(\xi(t)\) that is homoclinic to a hyperbolic saddle point \(z_0\), as well as some other technical hypotheses, they show that for small non-zero \(|\mu|\) there is
Dong, Xiujuan, Li, Yong
openaire   +2 more sources

RIGOROUS VERIFICATION OF THE EXISTENCE OF TRANSVERSAL HOMOCLINIC ORBITS

International Journal of Bifurcation and Chaos, 2008
In this paper we present a computer-assisted technique that allows us to prove rigorously that a transversal homoclinic orbit of discrete dynamical systems with this method is simpler than previous works on this subject.
openaire   +1 more source

Generating Chaos with Saddle-Focus Homoclinic Orbit

International Journal of Bifurcation and Chaos
This paper develops an anticontrol approach to design a 3D continuous-time autonomous chaotic system with saddle-focus homoclinic orbit, based on two chaotification criterions for all orbits to be globally bounded with positive Lyapunov exponents.
Chaoxia Zhang, Shangzhou Zhang, Yuqing Zhang   +2 more
openaire   +2 more sources

Infinity of minimal homoclinic orbits

Nonlinearity, 2011
The existence of homoclinic orbits for positive definite Lagrangians to hyperbolic tori (or Aubrey sets) has been proved by many authors. In this paper the author considers Lagrangian functions \(L\in C^2(TM\times \mathbb{R}, \mathbb{R})\) that are positive definite, have superlinear growth, are complete and \(1\)-periodic in the real factor.
openaire   +2 more sources

A Homoclinic Orbit for the Double Pendulum

1999
We consider a Hamiltonian system of two connected pendulums for the case of small mass of the second oscillator. We are interested in a homoclinic orbit for such system and present the equation for it.
openaire   +1 more source

Transversal Homoclinic Orbits

2022
openaire   +1 more source

Infinitely many homoclinic orbits for the second-order Hamiltonian systems

Applied Mathematics Letters, 2003
Zou Wenming
exaly  

Homoclinic orbits for second order self-adjoint difference equations

Journal of Mathematical Analysis and Applications, 2006
Zhiming Guo
exaly  

HOMOCLINIC ORBITS

1997
openaire   +1 more source