QUATERNION M SET WITH NONE ZERO CRITICAL POINTS

Fractals ◽  
2009 ◽  
Vol 17 (04) ◽  
pp. 427-439 ◽  
Author(s):  
YUAN-YUAN SUN ◽  
XING-YUAN WANG
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Julia Sets ◽  
Experimental Results ◽  
Stability Regions ◽  
Mandelbrot Sets ◽  
Efficient Information ◽  
The Stability ◽  
Detecting Method

The quaternion Mandelbrot sets (abbreviated as M sets) on the mapping f : z ← z2+ c with multiple critical points are constructed utilizing the cycle detecting method and the improved time escape algorithm. The topology structures and the fission evolutions of M sets are investigated, the boundaries and the centers of the stability regions are calculated, and the topology rules of the cycle orbits are discussed. The quaternion Julia sets with the parameter c selected from the M sets are constructed. It can be concluded that quaternion M sets have efficient information of the corresponding Julia sets. Experimental results demonstrate that the quaternion M sets with multiple critical points distinguish from that of zero critical point and the collection of the quaternion M sets with different critical points constitute the complete M sets on the mapping f : z ← z2+ c.

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

scholarly journals MEMBANGUN MODEL DINAMIS PENANGKARAN POPULASI MALEO (Macrochepalon Maleo) YANG MEMPERTAHANKAN EKSISTENSINYA DARI PREDATOR

2018 ◽  
Vol 15 (2) ◽  
pp. 144-156
Author(s):  
T Gusmawan ◽  
R Ratianingsih ◽  
N Nacong
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Captive Breeding ◽  
Growth Dynamics ◽  
Growth Cycle ◽  
Extinction Condition ◽  
Spawning Habitat ◽  
Conservation Areas ◽  
Free Zone ◽  
The Stability

Maleo (Macrocephalon maleo) is one of the endangered endemic species of Sulawesi due to diminishing spawning habitat, community exploitation and predators. The dynamic model of maleo population captivity to conserve its existence from predators is a mathematical model that describes the dynamics of maleo population growth cycle (M) with the threat of predators (P). In this study, the population of eggs maleo divided into two groups that are eggs in the free zone (Tb) and eggs in breeding (Tp). The eggs are in the captive breeding will be transfered to the exposure group (E). The model represents the interaction between the predators and populations reflecting maleo in each growth phase. The model has two critical points, namely the critical point 𝑇1 = ( 0,0,0,0, 𝜑 µ2 ) describing maleo extinction condition and critical point 𝑇2 = (𝑀∗ , 𝑇𝑝∗ ,𝐸 ∗ , 𝑇𝑏∗ , 𝑃 ∗ ) which describes the endemic conditions of maleo growth dynamics. The stability analysis shows that the system is unstable at both critical points. It is because the values of the first column in the Routh Hurwitz table changes in sign. Simulations of the endemic conditions showed that the maleo and egg populations in the free zone are decreasing with respect to time even though the exposed maleo still exist. The unstable endemic indicates that the existence of maleo breeding program in conservation areas still need another efforts support.

Modeling Stability in On-line Signatures

2014 ◽  
Vol 24 ◽  
pp. 37-46 ◽  
Author(s):  
Antonio Parziale ◽  
Salvatore G. Fuschetto ◽  
Angelo Marcelli
Keyword(s):  
Motor Control ◽  
Experimental Results ◽  
New Method ◽  
Signature Verification ◽  
Stability Regions ◽  
Proposed Model ◽  
On Line ◽  
The Stability ◽  
Definition Of ◽  
Handwriting Generation

A novel definition of stability regions and a new method for detecting them from on-line signatures is introduced in this paper. Building upon handwriting generation and motor control studies, the stability regions is defined as the longest similar sequences of strokes between a pair of genuine signatures. The stability regions are then used to select the most stable signatures, as well as to estimate the extent to which these stability regions are encountered in both genuine and simulated (forged) signatures, thus modeling the signing habit of a subject. Experimental results on the SUSig database show that the proposed model can be effectively used for signature verification. Purchase Article for $10 

scholarly journals MODEL MATEMATIKA KEARIFAN LOKAL MASYARAKATDESA TRUSMI DALAM MENJAGA EKSISTENSIKERAJINAN BATIK TULIS

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Arif Muchyidin
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Numerical Simulation ◽  
National Identity ◽  
Differential Equations ◽  
Critical Point ◽  
Critical Points ◽  
System Of Differential Equations ◽  
The Stability ◽  
The Village

Batik as an Indonesian national identity has contributed greatly to the Indonesian economy. However, the value of exports and other economic potentials are not supported by the number of batik, especially batik artisans in the village Trusmi. Trusmi batik artisans in the village is a craftsman who has been there all the time and remain there for generations. The phenomenon that occurs in the craft of batik Trusmi analyzed with mathematical modeling approach, in this case the dynamical system. From the resulting system of differential equations, then analyzed the stability around the critical point. From the resulting model, gained two critical points. The first critical point is a condition where there is no proficient craftmen (not expected), whereas at the second critical point is the potential of batik craftmen and proficient craftmen mutually exist, or in other words batik will still exist. From the results of numerical simulation, if , then batik Trusmi will still exist. However, if , then the number of proficient craftmen would quickly dwindle and slowly batik will be extinct.Key Words : dinamical system, critical points, stability

Critical point analysis of cubic ZnS

1970 ◽  
Vol 48 (21) ◽  
pp. 2477-2480 ◽  
Author(s):  
J. C. Irwin
Keyword(s):  
Theoretical Model ◽  
Critical Point ◽  
Infrared Spectra ◽  
Critical Points ◽  
Second Order ◽  
Experimental Results ◽  
Zone Boundary ◽  
Point Analysis ◽  
Critical Point Analysis

An interpretation of the second-order Raman and infrared spectra of cubic ZnS is given. A set of values is obtained for the phonon frequencies at the zone boundary critical points X, L, and W. These values are consistent with both the experimental results and a theoretical model. The frequencies obtained are compared with those proposed by previous workers.

Fractal Structures of General Mandelbrot Sets and Julia Sets Generated from Complex Non-Analytic Iteration Fm(z)=z¯m+c

2013 ◽  
Vol 347-350 ◽  
pp. 3019-3023
Author(s):  
De Jun Yan ◽  
Xiao Dan Wei ◽  
Hong Peng Zhang ◽  
Nan Jiang ◽  
Xiang Dong Liu
Keyword(s):  
Rotational Symmetry ◽  
Julia Sets ◽  
Boundary Curve ◽  
Mandelbrot Set ◽  
Escape Time ◽  
Fractal Structures ◽  
Mandelbrot Sets ◽  
The Stability ◽  
Definition Of ◽  
Analytic Iteration

In this paper we use the same idea as the complex analytic dynamics to study general Mandelbrot sets and Julia sets generated from the complex non-analytic iteration . The definition of the general critical point is given, which is of vital importance to the complex non-analytic dynamics. The general Mandelbrot set is proved to be bounded, axial symmetry by real axis, and have (m+1)-fold rotational symmetry. The stability condition of periodic orbits and the boundary curve of stability region of one-cycle are given. And the general Mandelbrot sets are constructed by the escape-time method and the periodic scanning algorithm, which present a better understanding of the structure of the Mandelbrot sets. The filled-in Julia sets Km,c have m-fold structures. Similar to the complex analytic dynamics, the general Mandelbrot sets are kinds of mathematical dictionary or atlas that map out the behavior of the filled-in Julia sets for different values of c.

scholarly journals MODEL MATEMATIKA KEARIFAN LOKAL MASYARAKATDESA TRUSMI DALAM MENJAGA EKSISTENSIKERAJINAN BATIK TULIS

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Arif Muchyidin
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Numerical Simulation ◽  
National Identity ◽  
Differential Equations ◽  
Critical Point ◽  
Critical Points ◽  
System Of Differential Equations ◽  
The Stability ◽  
The Village

Batik as an Indonesian national identity has contributed greatly to the Indonesian economy. However, the value of exports and other economic potentials are not supported by the number of batik, especially batik artisans in the village Trusmi. Trusmi batik artisans in the village is a craftsman who has been there all the time and remain there for generations. The phenomenon that occurs in the craft of batik Trusmi analyzed with mathematical modeling approach, in this case the dynamical system. From the resulting system of differential equations, then analyzed the stability around the critical point. From the resulting model, gained two critical points. The first critical point is a condition where there is no proficient craftmen (not expected), whereas at the second critical point is the potential of batik craftmen and proficient craftmen mutually exist, or in other words batik will still exist. From the results of numerical simulation, if , then batik Trusmi will still exist. However, if , then the number of proficient craftmen would quickly dwindle and slowly batik will be extinct.Key Words : dinamical system, critical points, stability

A Quasiperiodic Mathieu Equation

1995 ◽  
Author(s):  
Richard Rand ◽  
Rachel Hastings
Keyword(s):  
Numerical Integration ◽  
Mathieu Equation ◽  
Stability Regions ◽  
Regions Of Stability ◽  
Extensive Computation ◽  
The Stability ◽  
Direct Numerical Integration

Abstract In this work we investigate the following quasiperiodic Mathieu equation: x ¨ + ( δ + ϵ cos ⁡ t + ϵ cos ⁡ ω t ) x = 0 We use numerical integration to determine regions of stability in the δ–ω plane for fixed ϵ. Graphs of these stability regions are presented, based on extensive computation. In addition, we use perturbations to obtain approximations for the stability regions near δ=14 for small ω, and we compare the results with those of direct numerical integration.

scholarly journals STABILITY OF HIGH DENSITY CUBES IN RUBBLE MOUND BREAKWATERS

2020 ◽  
pp. 4
Author(s):  
Yalcin Yuksel ◽  
Marcel van Gent ◽  
Esin Cevik ◽  
H. Alper Kaya ◽  
Irem Gumuscu ◽  
...  
Keyword(s):  
Relative Density ◽  
Slope Angle ◽  
High Density ◽  
Experimental Results ◽  
Normal Density ◽  
Stability Number ◽  
Damage Initiation ◽  
Rubble Mound ◽  
The Stability ◽  
Rubble Mound Breakwaters

The stability number for rubble mound breakwaters is a function of several parameters and depends on unit shape, placing method, slope angle, relative density, etc. In this study two different densities for cubes in breakwater armour layers were tested to determine the influence of the density on the stability. The experimental results show that the stability of high density blocks were found to be more stable and the damage initiation for high density blocks started at higher stability numbers compared to normal density cubes.

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