Results 201 to 210 of about 5,743 (240)

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
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STOCHASTIC AVERAGING NEAR LONG HETEROCLINIC ORBITS

Stochastics and Dynamics, 2007
We refine some of the bounds of [10]. There, we considered the effect of diffusive perturbations on a two-dimensional ODE with a heteroclinic cycle. We constructed corrector functions for asymptotically "glueing" together behavior of periodic orbits in the boundary layer near the heteroclinic cycle.
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Orbits heteroclinic to invariant manifolds

Acta Mathematica Sinica, 1996
The persistence and the transversality of orbits heteroclinic (or homoclinic) to normally hyperbolic invariant manifolds are studied. The obtained results extend and improve some classical results (Wiggins and Yamashita) in the theory of dynamical systems on smooth manifolds.
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Approximating sequences for heteroclinic orbits

Mathematical Methods in the Applied Sciences, 1994
AbstractIn this paper we construct two approximating sequences for heteroclinic solution to a scalar ODE. These sequences do not ‘intersect’ and bound a unique real solution from below and above, thus enabling us to estimate this solution with any accuracy.
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Large heteroclinic orbits for some evolution equations

Nonlinear Analysis: Theory, Methods & Applications, 1988
We deal with the existence of heteroclinic orbits for a semilinear elliptic equation with boundary conditions on an unbounded domain. In particular, we consider a problem like \[ -\Delta u+f(u)=0\quad in\quad S;\quad u=0\quad on\quad \partial S \] where S is a strip, \(S={\mathbb{R}}\times \Omega\) with \(\Omega \subset {\mathbb{R}}^ n\) a bounded ...
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BIFURCATION OF ROUGH HETEROCLINIC LOOP WITH ORBIT FLIPS

International Journal of Bifurcation and Chaos, 2012
In this paper, heteroclinic loop bifurcations with double orbit flips are investigated in four-dimensional vector fields. We obtain the bifurcation equations by setting up a local coordinate system near the rough heteroclinic orbit and establishing the Poincaré map.
Liu, Xingbo, Wang, Zhenzhen, Zhu, Deming
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SHIL'NIKOV HETEROCLINIC ORBITS IN A CHAOTIC SYSTEM

International Journal of Modern Physics B, 2007
In this paper, a chaotic system which exhibits a chaotic attractor with only three equilibria for some parameters is considered. The existence of heteroclinic orbits of the Shil'nikov type in a chaotic system has been proved using the undetermined coefficient method. As a result, the Shil'nikov criterion guarantees that the system has Smale horseshoes.
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ON HOMOCLINIC AND HETEROCLINIC ORBITS OF CHEN'S SYSTEM

International Journal of Bifurcation and Chaos, 2006
We study the problem of existence of homoclinic and heteroclinic orbits of Chen's system. For the case of 2c > a > c > 0 and b ≥ 2a, we prove that the system has no homoclinic orbit but has two and only two heteroclinic orbits.
Li, Tiecheng, Chen, Guoting, Chen, Guanrong   +2 more
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Applying Lin's method to constructing heteroclinic orbits near the heteroclinic chain

Mathematical Methods in the Applied Sciences
In this paper, we apply Lin's method to study the existence of heteroclinic orbits near the degenerate heteroclinic chain under ‐dimensional periodic perturbations. The heteroclinic chain consists of two degenerate heteroclinic orbits and connected by three hyperbolic saddle points .
Bin Long, Yiying Yang
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Infinitely Many Heteroclinic Orbits of a Complex Lorenz System

International Journal of Bifurcation and Chaos, 2017
The existence of heteroclinic orbits of a chaotic system is a difficult yet interesting mathematical problem. Nowadays, a rigorous analytical proof for the existence of a heteroclinic orbit can be carried out only for some special chaotic and hyperchaotic systems, and few results are known for the complex systems.
Wang, Haijun, Li, Xianyi
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