BI-SPIRALING HOMOCLINIC CURVES AROUND A T-POINT IN CHUA'S EQUATION

2004 ◽  
Vol 14 (05) ◽  
pp. 1789-1793 ◽  
Author(s):  
FERNANDO FERNÁNDEZ-SÁNCHEZ ◽  
EMILIO FREIRE ◽  
ALEJANDRO J. RODRÍGUEZ-LUIS
Keyword(s):  
Two Dimensional ◽  
Homoclinic Connections ◽  
Parameter Bifurcation

In this work, the existence of curves of homoclinic connections that bi-spiral around a T-point between two saddle-focus equilibria is detected in Chua's equation. That is, the homoclinic curve emerges spiraling from a T-point in a parameter bifurcation plane and ends, by a different spiral, at the same T-point. This new phenomenon is related to the existence of more than one intersection between the two-dimensional manifolds of the involved equilibria at the T-point.

Analysis and study of two‐dimensional parameter bifurcation of wind power farms and composite loads

Wind Energy ◽  
2019 ◽  
Author(s):  
Abdelaziz Salah Saidi ◽  
Marwa Ben Slimene ◽  
Mohamed Arbi Khlifi ◽  
Mohammad Fazle Azeem ◽  
Salah Al Ahmadi ◽  
...  
Keyword(s):  
Wind Power ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Parameter Bifurcation ◽  
Analysis And Study

RESONANT GLUING BIFURCATIONS

2000 ◽  
Vol 10 (09) ◽  
pp. 2141-2160 ◽  
Author(s):  
ROBERT W. GHRIST
Keyword(s):  
Saddle Point ◽  
Parameter Space ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Centre Manifold ◽  
Principal Eigenvalues ◽  
Homoclinic Connections ◽  
Homoclinic Bifurcations ◽  
Zero Entropy

We consider the codimension-three phenomenon of homoclinic bifurcations of flows containing a pair of orbits homoclinic to a saddle point whose principal eigenvalues are in resonance. We concentrate upon the simplest possible configuration, the so-called "figure-of-eight," and reduce the dynamics near the homoclinic connections to those on a two-dimensional locally invariant centre manifold. The ensuing resonant gluing bifurcations exhibit features of both gluing bifurcations and resonant homoclinic bifurcations. Under certain twist conditions, the bifurcation structure is extremely rich, although describing zero-entropy flows. The analysis carefully exploits the topology of the orbits, the centre manifold and the parameter space.

scholarly journals Unfolding Codimension-Two Subsumed Homoclinic Connections in Two-Dimensional Piecewise-Linear Maps

2020 ◽  
Vol 30 (03) ◽  
pp. 2030006 ◽  
Author(s):  
David J. W. Simpson
Keyword(s):  
Periodic Solution ◽  
Piecewise Linear ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Codimension Two ◽  
Codimension One ◽  
Border Collision Bifurcations ◽  
Homoclinic Connections ◽  
Linear Maps ◽  
Piecewise Linear Maps

For piecewise-linear maps, the phenomenon that a branch of a one-dimensional unstable manifold of a periodic solution is completely contained in its stable manifold is codimension-two. Unlike codimension-one homoclinic corners, such “subsumed” homoclinic connections can be associated with stable periodic solutions. The purpose of this paper is to determine the dynamics near a generic subsumed homoclinic connection in two dimensions. Assuming the eigenvalues associated with the periodic solution satisfy [Formula: see text], in a two-parameter unfolding there exists an infinite sequence of roughly triangular regions within which the map has a stable single-round periodic solution. The result applies to both discontinuous and continuous maps, although these cases admit different characterizations for the border-collision bifurcations that correspond to boundaries of the regions. The result is illustrated with a discontinuous map of Mira and the two-dimensional border-collision normal form.

GLOBAL BIFURCATIONS OF CLOSED INVARIANT CURVES IN TWO-DIMENSIONAL MAPS: A COMPUTER ASSISTED STUDY

2005 ◽  
Vol 15 (04) ◽  
pp. 1285-1328 ◽  
Author(s):  
ANNA AGLIARI ◽  
GIAN-ITALO BISCHI ◽  
ROBERTO DIECI ◽  
LAURA GARDINI
Keyword(s):  
Computer Assisted ◽  
Flip Bifurcation ◽  
Two Dimensional ◽  
Global Bifurcations ◽  
Invariant Curves ◽  
Dimensional Parameter ◽  
Bifurcation Phenomena ◽  
Homoclinic Connections ◽  
Homoclinic Tangles ◽  
Qualitative Phase

In this paper we describe some sequences of global bifurcations involving attracting and repelling closed invariant curves of two-dimensional maps that have a fixed point which may lose stability both via a supercritical Neimark bifurcation and a supercritical pitchfork or flip bifurcation. These bifurcations, characterized by the creation of heteroclinic and homoclinic connections or homoclinic tangles, are first described through qualitative phase diagrams and then by several numerical examples. Similar bifurcation phenomena can also be observed when the parameters in a two-dimensional parameter plane cross through many overlapping Arnold's tongues.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Analysis of the 9th November 1990 flare

2000 ◽  
Vol 179 ◽  
pp. 229-232
Author(s):  
Anita Joshi ◽  
Wahab Uddin
Keyword(s):  
Image Processing ◽  
Two Dimensional ◽  
Temporal Behaviour ◽  
Contour Maps ◽  
Dimensional Measurements ◽  
Processing Software ◽  
Image Processing Software

AbstractIn this paper we present complete two-dimensional measurements of the observed brightness of the 9th November 1990Hαflare, using a PDS microdensitometer scanner and image processing software MIDAS. The resulting isophotal contour maps, were used to describe morphological-cum-temporal behaviour of the flare and also the kernels of the flare. Correlation of theHαflare with SXR and MW radiations were also studied.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

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