scholarly journals A Study on the double crisis vertex in a twoparameter plane*

2002 ◽  
Vol 51 (12) ◽  
pp. 2694
Author(s):  
Hong Ling ◽  
Xu Jian-Xue
Keyword(s):  
Parameter Plane ◽  
Two Parameter

Bifurcation and evolution of a forced and damped Duffing system in two-parameter plane

2018 ◽  
Vol 93 (2) ◽  
pp. 749-766 ◽  
Author(s):  
Jian-Fei Shi ◽  
Yan-Long Zhang ◽  
Xiang-Feng Gou
Keyword(s):  
Parameter Plane ◽  
Duffing System ◽  
Two Parameter

On the Parameter Plane of Nonlinear Coupled Oscillators

1993 ◽  
Vol 48 (5-6) ◽  
pp. 655-662
Author(s):  
Wolfgang Metzler ◽  
Achim Brelle ◽  
Klaus-Dieter Schmidt ◽  
Gerrit Danker ◽  
Matthias Köppe ◽  
...  
Keyword(s):  
Coupled Oscillators ◽  
Nonlinear Oscillator ◽  
Mandelbrot Set ◽  
Parameter Plane ◽  
Two Dimensional ◽  
Routes To Chaos ◽  
Nonlinear Coupled Oscillators ◽  
Two Parameter

Abstract Two well-known bifurcation routes to chaos of two-dimensional coupled logistic maps are embedded in a two-parameter plane of a canonical nonlinear oscillator which contains a non-analytic analogon to the Mandelbrot set.

NONSMOOTH AND SMOOTH BIFURCATIONS IN A DISCONTINUOUS PIECEWISE MAP

2012 ◽  
Vol 22 (05) ◽  
pp. 1250112 ◽  
Author(s):  
ZHIYING QIN ◽  
YUEJING ZHAO ◽  
JICHEN YANG
Keyword(s):  
Fixed Point ◽  
Bifurcation Diagram ◽  
Bifurcation Point ◽  
Peculiar Feature ◽  
Parameter Plane ◽  
Flip Bifurcation ◽  
Border Collision Bifurcation ◽  
Bifurcation Structures ◽  
Piecewise Map ◽  
Two Parameter

In this paper, a piecewise map with singularity of the power (-1/2) is introduced. For this piecewise map, there is an infinite discontinuous gap on the origin. The conditions of nonsmooth border-collision bifurcation and smooth fold or flip bifurcation are analytically derived. For period-1 fixed point, two-parameter-plane can be divided into seven ranges according to different bifurcation structures. For period-n orbits, codimension-2 bifurcation point may lead to different period-increment sequence, and a peculiar feature is found that there are two different period-increment sequences in the same bifurcation diagram.

Bifurcation and chaos analysis of spur gear pair in two-parameter plane

2014 ◽  
Vol 79 (3) ◽  
pp. 2225-2235 ◽  
Author(s):  
Xiang-Feng Gou ◽  
Ling-Yun Zhu ◽  
Dai-Lin Chen
Keyword(s):  
Spur Gear ◽  
Parameter Plane ◽  
Gear Pair ◽  
Bifurcation And Chaos ◽  
Chaos Analysis ◽  
Two Parameter

Low-Dimensional Discrete Kuramoto Model: Hierarchy of Multifrequency Quasiperiodicity Regimes

2014 ◽  
Vol 24 (07) ◽  
pp. 1430022 ◽  
Author(s):  
Alexander P. Kuznetsov ◽  
Yuliya V. Sedova
Keyword(s):  
Coupling Parameter ◽  
Kuramoto Model ◽  
Parameter Plane ◽  
Phase Oscillators ◽  
Repulsive Interactions ◽  
Discrete Phase ◽  
Model Hierarchy ◽  
Frequency Coupling ◽  
Low Dimensional ◽  
Two Parameter

The dynamics of a low-dimensional ensemble consisting of a network of five discrete phase oscillators is considered. A two-parameter synchronization picture, which appears instead of the Arnol'd tongues with an increase of the system dimension, is discussed. An appearance of the Arnol'd resonance web is detected on the "frequency–coupling" parameter plane. The cases of attractive and repulsive interactions are discussed.

scholarly journals Bifurcation Characteristics of Fundamental and Subharmonic Impact Motions of a Mechanical Vibration System with Motion Limiting Constraints on a Two-Parameter Plane

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Shijun Wang ◽  
Guanwei Luo
Keyword(s):  
Impact Velocity ◽  
Mechanical Vibration ◽  
Three Dimensional ◽  
Low Frequency ◽  
Parameter Plane ◽  
Force Frequency ◽  
Distribution Law ◽  
Rigid Constraint ◽  
Two Parameter ◽  
Dimensional Surface

A two-degree-of-freedom periodically forced system with multiple gaps and rigid constraints is studied. Multiple types of impact vibrations occur at each rigid constraint and interact with each other, which results in the emergence of some complex transitions in the system. Through the cosimulation of the key parameters gap value δ between the two masses and the excitation force frequency ω, the types, existence areas, and bifurcation regularities of the periodic and subharmonic motions can be obtained on the (ω, δ)-parameter plane. In the corresponding three-dimensional surface diagram of the maximum impact velocity, the distribution law of the maximum impact velocity at each constraint can be obtained. The transition laws of fundamental impact motions in the low-frequency parameter domain are studied, and two types of transition regions in the transitions of adjacent fundamental impact motions are found: tongue-like regions and hysteresis regions. Moreover, these two types of transition regions show some atypical partitioning and deformation due to the combined effects of impact vibrations at each constraint. By combining the two-parameter plane diagram and the three-dimensional surface diagram, the effect of changing the gap values between each mass and the fixed constraint and the damping coefficient ζ on the dynamic characteristics of the system is studied. Combining the existence areas of periodic motions and the distribution of maximum impact velocity can provide guidance for the reasonable selection of system parameters.

Some results of the Barbier-Chalonge-Divan system of stellar classification

1966 ◽  
Vol 24 ◽  
pp. 77-90 ◽  
Author(s):  
D. Chalonge
Keyword(s):  
Early Type ◽  
Parameter System ◽  
Early Type Stars ◽  
Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

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