Results 181 to 190 of about 10,271 (227)

Symbolic Quest into Homoclinic Chaos

International Journal of Bifurcation and Chaos, 2014
We explore the multifractal, self-similar organization of heteroclinic and homoclinic bifurcations of saddle singularities in the parameter space of the Shimizu–Morioka model that exhibits the Lorenz chaotic attractor. We show that complex transformations that underlie the transitions from the Lorenz attractor to wildly chaotic dynamics are ...
T. Xing, R. Barrio, A. Shilnikov
semanticscholar   +2 more sources

Limit cycle bifurcations near homoclinic and heteroclinic loops via stability-changing of a homoclinic loop

Chaos, Solitons and Fractals, 2015
Maoan Han, Yanqin Xiong
exaly   +2 more sources

Controlling homoclinic orbits

Theoretical and Computational Fluid Dynamics, 1989
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bloch, A. M., Marsden, J. E.
openaire   +3 more sources

Nonlocal nonlinear chaotic and homoclinic analysis of double layered forced viscoelastic nanoplates

Mechanical systems and signal processing, 2019
The homoclinic phenomena and chaotic motions of the forced double layered nanoplates (DLNP) are investigated. By the nonlocal theory, the nonlinear equations of motion of DLNP subjected to transverse harmonic excitation are established.
Yu Wang, Fengming Li, Haisheng Shu
semanticscholar   +1 more source

On homoclinic tangencies, hyperbolicity, creation of homoclinic orbits and variation of entropy

Nonlinearity, 2000
This paper generalizes a result of \textit{J.-M. Gambaudo} and \textit{J. Rocha} [ibid. 7, 1251-1259 (1994; Zbl 0806.58031), Erratum 12, 443 (1999; Zbl 0959.37028)], which gave sufficient conditions for a diffeomorphism on the 2-sphere to be \(C^1\) approximated by another exhibiting a homoclinic point, using an unproved theorem of Araújo and Mané. The
Pujals, Enrique R., Sambarino, Martín
openaire   +1 more source

N-Homoclinic bifurcations for homoclinic orbits changing their twisting

Journal of Dynamics and Differential Equations, 1996
The author considers two-parameter families of vector fields possessing a homoclinic orbit along a path in the parameter plane. These homoclinic orbits are homoclinic to a hyperbolic singularity that has a one-dimensional unstable manifold. The weakest stable and unstable eigenvalues of the linearized vector field at the singularity are supposed to be ...
openaire   +2 more sources

On the quantisation of homoclinic motion

Nonlinearity, 1989
Summary: The density of states of a classically chaotic system can be represented as a sum over its periodic orbits. An unstable periodic orbit may be the limit of homoclinic orbits, that in turn accumulate infinite families of satellite periodic orbits with arbitrarily long periods.
openaire   +2 more sources

Homoclinic Explosions: The First Homoclinic Explosion

1982
When r > 1 there is a two-dimensional sheet of initial values in R3 from which trajectories tend towards the origin. This two-dimensional sheet is called the stable manifold of the origin. Near the origin we know that this sheet looks like a plane (the plane associated with the two negative eigenvalues of the flow linearized near the origin) and if we ...
openaire   +1 more source

Stability analysis and solutions of (2 + 1)-Kadomtsev–Petviashvili equation by homoclinic technique based on Hirota bilinear form

Nonlinear dynamics, 2022
A. Yokuş, M. Isah
semanticscholar   +1 more source

Rigorous Computations of Homoclinic Tangencies

SIAM Journal on Applied Dynamical Systems, 2006
In this paper, we propose a rigorous computational method for detecting homoclinic tangencies and structurally unstable connecting orbits. It is a combination of several tools and algorithms, including the interval arithmetic, the subdivision algorithm, the Conley index theory, and the computational homology theory.
Zin Arai, Konstantin Mischaikow
openaire   +1 more source