Wada bifurcations and partially Wada basin boundaries in a two-dimensional cubic map

2013 ◽  
Vol 377 (18) ◽  
pp. 1274-1281 ◽  
Author(s):  
Yongxiang Zhang ◽  
Guanwei Luo
Keyword(s):  
Two Dimensional ◽  
Basin Boundaries

ABOUT TWO-DIMENSIONAL PIECEWISE CONTINUOUS NONINVERTIBLE MAPS

1996 ◽  
Vol 06 (05) ◽  
pp. 893-918 ◽  
Author(s):  
MIRA CHRISTIAN
Keyword(s):  
Two Dimensional ◽  
Line Of Discontinuity ◽  
Piecewise Continuous ◽  
Noninvertible Maps ◽  
Basin Boundaries

This paper is devoted to some features of a class of two-dimensional piecewise continuous noninvertible maps, with only one line of discontinuity. It describes properties of basin boundaries, chaotic areas, and their bifurcations. Such properties are not encountered with continuous noninvertible maps.

Bifurcational Mechanism of Multistability Formation and Frequency Entrainment in a van der Pol Oscillator with an Additional Oscillatory Circuit

2016 ◽  
Vol 26 (07) ◽  
pp. 1650124 ◽  
Author(s):  
Sergey Astakhov ◽  
Oleg Astakhov ◽  
Vladimir Astakhov ◽  
Jürgen Kurths
Keyword(s):  
Hopf Bifurcation ◽  
Invariant Manifolds ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Oscillatory Circuit ◽  
Van Der Pol ◽  
Frequency Entrainment ◽  
Basin Boundaries

In this paper, the bifurcational mechanism of frequency entrainment in a van der Pol oscillator coupled with an additional oscillatory circuit is studied. It is shown that bistability observed in the system is based on two bifurcations: a supercritical Andronov–Hopf bifurcation and a sub-critical Neimark–Sacker bifurcation. The attracting basin boundaries are determined by stable and unstable invariant manifolds of a saddle two-dimensional torus.

PLANE MAPS WITH DENOMINATOR I: SOME GENERIC PROPERTIES

1999 ◽  
Vol 09 (01) ◽  
pp. 119-153 ◽  
Author(s):  
GIAN-ITALO BISCHI ◽  
LAURA GARDINI ◽  
CHRISTIAN MIRA
Keyword(s):  
Invariant Sets ◽  
Two Dimensional ◽  
Focal Points ◽  
Generic Properties ◽  
New Concepts ◽  
Dynamical Properties ◽  
Basin Boundaries ◽  
Dynamic Phenomena

This paper is devoted to the study of some global dynamical properties and bifurcations of two-dimensional maps related to the presence, in the map or in one of its inverses, of a vanishing denominator. The new concepts of focal points and of prefocal curves are introduced in order to characterize some new kinds of contact bifurcations specific to maps with denominator. The occurrence of such bifurcations gives rise to new dynamic phenomena, and new structures of basin boundaries and invariant sets, whose presence can only be observed if a map (or some of its inverses) has a vanishing denominator.

Change of the fractal dimension of basin boundaries in a two-dimensional cubic map

1989 ◽  
Vol 142 (2-3) ◽  
pp. 95-98 ◽  
Author(s):  
Yoshihiro Yamaguchi ◽  
Kiyotaka Tanikawa
Keyword(s):  
Fractal Dimension ◽  
Two Dimensional ◽  
Basin Boundaries

On the Fractal Structure of Basin Boundaries in Two-Dimensional Noninvertible Maps

2003 ◽  
Vol 13 (07) ◽  
pp. 1767-1785 ◽  
Author(s):  
A. Agliari ◽  
L. Gardini ◽  
C. Mira
Keyword(s):  
Fractal Structure ◽  
Real Plane ◽  
Two Dimensional ◽  
Numerical Examples ◽  
The Real ◽  
Basin Boundary ◽  
Fractal Basin Boundary ◽  
Noninvertible Maps ◽  
Analytical Tools ◽  
Basin Boundaries

In this paper we give an example of transition to fractal basin boundary in a two-dimensional map coming from the applicative context, in which the hard-fractal structure can be rigorously proved. That is, not only via numerical examples, although theoretically guided, as often occurs in maps coming from the applications, but also via analytical tools. The proposed example connects the two-dimensional maps of the real plane to the well-known complex map.

ABRUPT DIMENSION CHANGES AT BASIN BOUNDARY METAMORPHOSES

1992 ◽  
Vol 02 (03) ◽  
pp. 533-541 ◽  
Author(s):  
BAE-SIG PARK ◽  
CELSO GREBOGI ◽  
YING-CHENG LAI
Keyword(s):  
Dynamical Systems ◽  
Numerical Experiments ◽  
System Parameter ◽  
Analytic Calculation ◽  
Two Dimensional ◽  
Qualitative Model ◽  
One Dimensional ◽  
Basin Boundary ◽  
Chaotic Dynamical Systems ◽  
Basin Boundaries

Basin boundaries in chaotic dynamical systems can be either smooth or fractal. As a system parameter changes, the structure of the basin boundary also changes. In particular, the dimension of the basin boundary changes continuously except when a basin boundary metamorphosis occurs, at which it can change abruptly. We present numerical experiments to demonstrate such sudden dimension changes. We have also used a one-dimensional analytic calculation and a two-dimensional qualitative model to explain such changes.

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.

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