CHAOS IN CROSS-COUPLED BVP OSCILLATORS

2005 ◽  
Vol 15 (10) ◽  
pp. 3359-3366 ◽  
Author(s):  
TETSUSHI UETA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
Periodic Solutions ◽  
Bifurcation Diagram ◽  
Coupled Oscillator ◽  
Chaotic Motions ◽  
Independent State ◽  
State Variable ◽  
Bifurcation Problems ◽  
The Cross

In this letter, we investigate the cross-coupled BVP oscillators. A single BVP oscillator has two terminals which can extract an independent state variable, so in the preceding works, several coupling systems have been studied. Synchronization modes and chaos in these systems are classified as results of bifurcation problems. We revisit a coupled oscillator, and clarify new results which have not been reported before, i.e. stable tori and its breakdown, and chaotic motions. Also classification of synchronized periodic solutions is done by a bifurcation diagram.

ABOUT THE PROBLEM OF CLASSIFICATION OF THE CONCEPTS OF INFORMATICS STUDIED AT SECONDARY SCHOOL

2018 ◽  
pp. 4-7
Author(s):  
S. I. Zenko
Keyword(s):  
Secondary School ◽  
Foreign Language ◽  
Computer Science ◽  
Parts Of Speech ◽  
The Third ◽  
The Cross ◽  
Definition Of

The article raises the problem of classification of the concepts of computer science and informatics studied at secondary school. The efficiency of creation of techniques of training of pupils in these concepts depends on its solution. The author proposes to consider classifications of the concepts of school informatics from four positions: on the cross-subject basis, the content lines of the educational subject "Informatics", the logical and structural interrelations and interactions of the studied concepts, the etymology of foreign-language and translated words in the definition of the concepts of informatics. As a result of the first classification general and special concepts are allocated; the second classification — inter-content and intra-content concepts; the third classification — stable (steady), expanding, key and auxiliary concepts; the fourth classification — concepts-nouns, conceptsverbs, concepts-adjectives and concepts — combinations of parts of speech.

Sand deformation under proportional loading

1986 ◽  
Vol 23 (2) ◽  
pp. 155-163 ◽  
Author(s):  
D. Negussey ◽  
Y. P. Vaid
Keyword(s):  
Relative Density ◽  
Triaxial Test ◽  
Stress Ratio ◽  
Proportional Loading ◽  
Stress Strain ◽  
Independent State ◽  
State Variable ◽  
Strain Components ◽  
Strain Relationship ◽  
Observed Behaviour

A fundamental experimental study of sand behaviour under low stress ratio proportional loading wherein all strain components are contractant is presented. Experimentally observed behaviour under stress conditions of the triaxial test led to a coherent framework for representing proportional loading stress–strain response. The stress–strain relationship formulated incorporates relative density as an inherent independent state variable and does not require appeal to material isotropy. Key words: triaxial test, proportional loading, sand, relative density, energy density, stress increment, strain increment.

scholarly journals Serological studies ofBacteroides fragilis

1977 ◽  
Vol 79 (2) ◽  
pp. 233-241 ◽  
Author(s):  
K. M. Elhag ◽  
K. A. Bettelheim ◽  
Soad Tabaqchali
Keyword(s):  
Bacteroides Fragilis ◽  
Gram Negative ◽  
Biochemical Characteristics ◽  
Cross Reactions ◽  
Homologous Antigen ◽  
Specific Antisera ◽  
Serological Studies ◽  
The Cross ◽  
O Antigens

SUMMARYUsing direct agglutination methods, a simple serological scheme for the classification ofBacteroides fragilisis described. Twenty strains ofB. fragiliswere selected by a process of successive screening from 151 strains obtained from various sources. O-antigens were prepared from the 20 strains, and used to raise antisera in rabbits.Each of the 20 antisera reacted with its homologous antigen and eight antisera cross-reacted with other subspecies. These cross-reactions were successfully removed after absorption of the antisera with the cross-reacting antigens, resulting in 19 type-specific antisera, titres ranging from 40 to 320, and 19 distinct serotypes ofB. fragilis. There was no correlation between the antigenic and the biochemical characteristics of these strains and no cross-reactions occurred with other gram-negative anaerobes,B. melaninogenicus, Sphaerophorus necrophorusandFuso-bacterium necrogenes.

scholarly journals BIFURCATIONS AND CHAOS IN A PERIODIC PREDATOR-PREY MODEL

1992 ◽  
Vol 02 (01) ◽  
pp. 117-128 ◽  
Author(s):  
YU.A. KUZNETSOV ◽  
S. MURATORI ◽  
S. RINALDI
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Bifurcation Diagram ◽  
Local Theory ◽  
Predator Prey ◽  
Varying Parameters ◽  
Routes To Chaos ◽  
Predator Prey Model ◽  
Prey Model ◽  
Continuation Technique

The model most often used by ecologists to describe interactions between predator and prey populations is analyzed in this paper with reference to the case of periodically varying parameters. A complete bifurcation diagram for periodic solutions of period one and two is obtained by means of a continuation technique. The results perfectly agree with the local theory of periodically forced Hopf bifurcation. The two classical routes to chaos, i.e., cascade of period doublings and torus destruction, are numerically detected.

scholarly journals A Periodic Problem of a Semilinear Pseudoparabolic Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-27 ◽  
Author(s):  
Yang Cao ◽  
Jingxue Yin ◽  
Chunhua Jin
Keyword(s):  
Periodic Solutions ◽  
Periodic Problem ◽  
Complete Classification ◽  
Pseudoparabolic Equation ◽  
Periodic Problems ◽  
Existence And Nonexistence

A class of periodic problems of pseudoparabolic type equations with nonlinear periodic sources are investigated. A rather complete classification of the exponentpis given, in terms of the existence and nonexistence of nontrivial and nonnegative periodic solutions.

Research on Recognition of Pathological Voice by AD Tree

2013 ◽  
Vol 658 ◽  
pp. 647-651 ◽  
Author(s):  
Jun Jie Zhu ◽  
Xiao Jun Zhang ◽  
Ji Hua Gu ◽  
He Ming Zhao ◽  
Qiang Zhou ◽  
...  
Keyword(s):  
Cross Validation ◽  
Recognition Rate ◽  
Experimental Results ◽  
Acoustic Features ◽  
Recognition Process ◽  
Normal Voice ◽  
The Cross ◽  
Fold Cross Validation ◽  
Pathological Voice

This paper mainly studies on the classification of pathological voice from normal voice based on the sustained vowel /a/. Firstly, the original 18 acoustic features are extracted. Then on the basis of the extracted parameters, this paper recognizes the pathological voice using AD Tree. During the classification stage, the cross-validation of features is also as references in the process. This method is validated with a sound database provided by the Massachusetts Eye and Ear Infirmary (MEEI). After the 10 fold cross-validation, comparing with 7 other kinds of classifiers, the experimental results show that AD Tree can get the highest recognition rate of 95.2%. The method in this paper shows that all the extracted parameters are reasonable in the following recognition process and AD tree is a good recognition way in pathological voice research.

Multiple Solutions in an Amplitude Limited Jeffcott Rotor Including Rubbing and Stick-Slip Effect

2005 ◽  
Author(s):  
Jan-Olov Aidanpa¨a¨
Keyword(s):  
Bifurcation Diagram ◽  
Contact Stiffness ◽  
Damping Ratio ◽  
Slip Effect ◽  
Chaotic Motions ◽  
Stick Slip ◽  
Diagram Method ◽  
Machine Failure ◽  
Jeffcott Rotor ◽  
Stable Solutions

The non-linear behaviour of rub-impact rotors have been studied in several papers. In such systems rich dynamics have been found together with the coexistence of solutions within some specific parameter ranges. In this paper an attempt is made to find all stable solutions for an amplitude limited Jeffcott rotor including rubbing and stick-slip effect. The recently suggested “multi bifurcation diagram method” is used to find and extract stable sets of bifurcation diagrams. A system is chosen where the linear stationary amplitude only exceeds the clearance in a narrow region near the natural frequency. Therefore large regions in frequency are expected to have only the linear stationary response. The results show that it is only for very low frequencies that one single solution exists. Even though periodic motions are dominant, there exist large ranges in frequency with quasi-periodic or chaotic motions. For the studied cases, three coexisting stable solutions are most common. In one case as many as four stable solutions was found to coexist. For rotors with large clearances (no impacts necessary) it is still possible to find several coexisting motions. For all cases the stick motion is the most severe one with large amplitudes and high backward whirl frequencies. In real situations the consequence of this stick motion is machine failure. These high amplitude motions were found to be stable over large frequency ranges. From the stability analysis it was found that this rolling motion can be avoided by low spin speed, low contact stiffness, low coefficient of friction, small ratio of disc radius/clearance or high damping ratio. In a design situation the parameters are seldom known with high accuracy. Therefore, it is of interest to know all solutions for parameter intervals. The multi-bifurcation diagram can be used in such situations to design a robust machine or at least be prepared for unwanted dynamics.

BIFURCATION BEHAVIORS OF THE TWO-STATE VARIABLE FRICTION LAW OF A ROCK MASS SYSTEM

2013 ◽  
Vol 23 (11) ◽  
pp. 1350184 ◽  
Author(s):  
GAO XUEJUN
Keyword(s):  
Rock Mass ◽  
Equilibrium Position ◽  
Continuation Method ◽  
Chaotic Motions ◽  
Mass System ◽  
Stick Slip ◽  
Hopf Bifurcation Point ◽  
Friction Law ◽  
State Variable ◽  
Variable Friction

Based on the stability and bifurcation theory of dynamical systems, the bifurcation behaviors and chaotic motions of the two-state variable friction law of a rock mass system are investigated by the bifurcation diagrams based on the continuation method and the Poincaré maps. The stick-slip of the rock mass is formulated as an initial values problem for an autonomous system of three coupled nonlinear ordinary differential equations (ODEs) of first order. The results of linear stability analysis indicate that there is an equilibrium position in the rock mass system. Furthermore, numerical results of nonlinear analysis indicate that the equilibrium position loses its stability from a sup-critical Hopf bifurcation point, and then the bifurcating periodic motion evolves into chaotic motion through a series of period-doubling bifurcations with the decreasing of the control parameter. The stick-slip and chaotic motions evolve into infinity in the end with some unstable periodic motions.

scholarly journals NONDEGENERATE UMBILICS, THE PATH FORMULATION AND GRADIENT BIFURCATION PROBLEMS

2009 ◽  
Vol 19 (09) ◽  
pp. 2965-2977 ◽  
Author(s):  
JACQUES-ELIE FURTER ◽  
ANGELA MARIA SITTA
Keyword(s):  
Cylindrical Panel ◽  
Point Of View ◽  
Singular Behavior ◽  
Universal Unfolding ◽  
Buckling Modes ◽  
The Core ◽  
Bifurcation Problems ◽  
Multiparameter Bifurcation ◽  
Special Parameter

Parametrized contact-equivalence is a successful theory for the understanding and classification of the qualitative local behavior of bifurcation diagrams and their perturbations. Path formulation is an alternative point of view making explicit the singular behavior due to the core of the bifurcation germ (when the parameters vanish) from the effects of the way parameters enter. We show how to use path formulation to classify and structure efficiently multiparameter bifurcation problems in corank 2 problems. In particular, the nondegenerate umbilics singularities are the generic cores in four situations: the general or gradient problems, with or without ℤ2 symmetry where ℤ2 acts on the second component of ℝ2 via κ(x,y) = (x,-y). The universal unfolding of the umbilic singularities have an interesting "Russian doll" type of structure of miniversal unfoldings in all those categories. With the path formulation approach we can handle one, or more, parameter situations using the same framework. We can even consider some special parameter structure (for instance, some internal hierarchy of parameters). We classify the generic bifurcations with 1, 2 or 3 parameters that occur in those cases. Some results are known with one bifurcation parameter, but the others are new. We discuss some applications to the bifurcation of a loaded cylindrical panel. This problem has many natural parameters that provide concrete examples of our generic diagrams around the first interaction of the buckling modes.

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