ENERGY-LIKE FUNCTIONS FOR SOME DISSIPATIVE CHAOTIC SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2507-2521 ◽  
Author(s):  
C. SARASOLA ◽  
A. D'ANJOU ◽  
F. J. TORREALDEA ◽  
A. MOUJAHID
Keyword(s):  
Phase Space ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Chaotic Systems ◽  
Quantitative Measure ◽  
Energy Functions ◽  
Dissipation Of Energy ◽  
Rossler System ◽  
Order Polynomial ◽  
Fourth Order Polynomial

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lü–Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the Rössler system at least a fourth-order polynomial is required to properly represent its energy.

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

scholarly journals An Improved Analysis for the Harmonic Distortion of MOS Voltage-Controlled-Resistors

1997 ◽  
Vol 19 (4) ◽  
pp. 253-260
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Fourth Order ◽  
Harmonic Distortion ◽  
Voltage Characteristic ◽  
Current Voltage Characteristic ◽  
Mos Transistor ◽  
Current Voltage ◽  
Order Polynomial ◽  
Polynomial Expression ◽  
Analytical Expressions ◽  
Fourth Order Polynomial

In this paper, a fourth-order polynomial expression is obtained for the nonlinear current-voltage characteristic of a MOS transistor operating in the triode region. Using this expression, closed-form expressions are obtained for the second-, third- and fourth-harmonic distortion of a MOS voltage-controlled- resistors. The analytical expressions obtained in this paper can be used for a quantitative study of the effect of different parameters of the performance of MOS voltage-controlled-resistors.

scholarly journals Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators

1997 ◽  
Vol 12 (15) ◽  
pp. 2725-2739 ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Quantum Mechanics ◽  
Fourth Order ◽  
Classification Scheme ◽  
Algebraic Expression ◽  
Topological Invariants ◽  
Square Root ◽  
Fredholm Operators ◽  
Compatibility Conditions ◽  
Order Polynomial ◽  
Fourth Order Polynomial

The general features of the degeneracy structure of (p = 2) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric systems whose Hamiltonian is the square root of a fourth order polynomial in the generators of the parasupersymmetry. These systems are interesting to study for they lead to the introduction of a set of topological invariants very similar to the Witten indices of ordinary supersymmetric quantum mechanics. The topological invariants associated with parasupersymmetry are shown to be related to a pair of Fredholm operators satisfying two compatibility conditions. An explicit algebraic expression for the topological invariants of a class of parasupersymmetric systems is provided.

CHAOS SYNCHRONIZATION VIA CONTROLLING PARTIAL STATE OF CHAOTIC SYSTEMS

2001 ◽  
Vol 11 (06) ◽  
pp. 1737-1741 ◽  
Author(s):  
XINGHUO YU ◽  
YANXING SONG
Keyword(s):  
Invariant Manifold ◽  
Fourth Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Dynamic Properties ◽  
Rossler System ◽  
Rössler System ◽  
Partial State ◽  
The Lorenz System

An invariant manifold based chaos synchronization approach is proposed in this letter. A novel idea of using only a partial state of chaotic systems to synchronize the coupled chaotic systems is presented by taking into account the inherent dynamic properties of the chaotic systems. The effectiveness of the approach and idea is tested on the Lorenz system and the fourth-order Rossler system.

Analytical method for locating the secondary instant centres of indeterminate planar linkages

2008 ◽  
Vol 223 (2) ◽  
pp. 491-502 ◽  
Author(s):  
C-M Kung ◽  
L-C T Wang
Keyword(s):  
Fourth Order ◽  
Analytical Method ◽  
Polynomial Equation ◽  
Automated Analysis ◽  
Numerical Examples ◽  
Order Polynomial ◽  
Velocity Information ◽  
Planar Linkages ◽  
Fourth Order Polynomial ◽  
Order Polynomial Equation

This article presents a new analytical method for locating secondary instant centres (SICs) of indeterminate planar linkages. In this method the SICs are first discriminated into three classes according to their level of geometric dependencies. The concepts of instant-centre digraph, instant-centre walk, and instant-centre circuit are then introduced to establish the recursive relationships between the classified instant centres. It is shown that the location of the instant centres within an instant-centre circuit can be evaluated recursively by first solving a second-order polynomial equation. In addition, by combining the recurrence conditions of several related instant-centre walks, the locations of SICs that are not within an instant-centre circuit can be solved analytically from a fourth-order polynomial equation. The proposed method does not rely on any velocity information or graphical techniques; therefore, it can be applied systematically to all types of indeterminate linkages. It can also be implemented on digital computers for automated analysis. Three numerical examples are presented to demonstrate the usage of this method.

Displacement Analysis of the Generalized Clemens Coupling, The R-R-S-R-R Spatial Linkage

1975 ◽  
Vol 97 (2) ◽  
pp. 575-580 ◽  
Author(s):  
D. M. Wallace ◽  
F. Freudenstein
Keyword(s):  
Fourth Order ◽  
Constant Velocity ◽  
Degrees Of Freedom ◽  
Input Output ◽  
Closed Form Solutions ◽  
Input And Output ◽  
Order Polynomial ◽  
Special Case ◽  
Output Equation ◽  
Fourth Order Polynomial

The Clemens Coupling is a constant-velocity, universal-type joint for nonparallel intersecting shafts. This mechanism is a spatial linkage with five links connected by four revolute pairs, R, and one spherical pair (ball-and-socket joint), S, which is located symmetrically with respect to the input and output shafts. The Clemens Coupling is a special case of the R-R-S-R-R spatial linkage with general proportions, which will, therefore, be called the Generalized Clemens Coupling. This paper gives the algebraic derivation of the input-output equation for the general R-R-S-R-R linkage and demonstrates that it is a fourth-order polynomial in the half tangents of the crank angles. The effect of housing-error tolerances on the displacements of the Clemens Coupling has also been considered. The results demonstrate feasibility of closed-form solutions for five-link mechanisms with kinematic pairs having more than two degrees of freedom.

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