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

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

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.

A 3D Autonomous System with Infinitely Many Chaotic Attractors

2019 ◽  
Vol 29 (12) ◽  
pp. 1950166 ◽  
Author(s):  
Ting Yang ◽  
Qigui Yang
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Autonomous System ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Double Zero ◽  
Finite Dimensional ◽  
Periodic Attractors ◽  
The Stability ◽  
Autonomous Dynamical System

Intuitively, a finite-dimensional autonomous system of ordinary differential equations can only generate finitely many chaotic attractors. Amazingly, however, this paper finds a three-dimensional autonomous dynamical system that can generate infinitely many chaotic attractors. Specifically, this system can generate infinitely many coexisting chaotic attractors and infinitely many coexisting periodic attractors in the following three cases: (i) no equilibria, (ii) only infinitely many nonhyperbolic double-zero equilibria, and (iii) both infinitely many hyperbolic saddles and nonhyperbolic pure-imaginary equilibria. By analyzing the stability of double-zero and pure-imaginary equilibria, it is shown that the classic Shil’nikov criteria fail in verifying the existence of chaos in the above three cases.

scholarly journals Stability and phase space analysis in f(R) theory with generalized exponential f(R) model

2016 ◽  
Vol 25 (10) ◽  
pp. 1650098 ◽  
Author(s):  
R. D. Boko ◽  
M. J. S. Houndjo ◽  
J. Tossa
Keyword(s):  
Dynamical System ◽  
Power Law ◽  
Critical Points ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Stability Conditions ◽  
De Sitter ◽  
Text Model ◽  
The Stability ◽  
Specific Phase

We have studied in this paper, the stability of dynamical system in [Formula: see text] gravity. We have considered the [Formula: see text] [Formula: see text]-gravity and explored its dynamical analysis. We found six critical points among which only one describes a universe filled of both matter and dominated dark energy. It is shown that these critical points present specific phase spaces described by the corresponding fluids. Furthermore, we have investigated the stability conditions of these critical points and find that these conditions are dependent of the model parameters. We also study the stability of a new power-law [Formula: see text] model with de Sitter and power law solutions.

scholarly journals METHODS OF OPTIMIZATION OF PARAMETRIC SYSTEMS

2021 ◽  
pp. 151-157
Author(s):  
V. T. Matvienko ◽  
V. V. Pichkur ◽  
D. I. Cherniy
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Gradient Descent ◽  
Parametric Optimization ◽  
Sensitivity Function ◽  
System Of Differential Equations ◽  
Parametric System ◽  
Gradient Of The Functional ◽  
Parametric Systems

The paper considers methods of parametric optimization of a dynamical system, which is described by a parametric system of differential equations. The gradient of the functional in the form of Boltz is found, which is the basis of methods such as gradient descent. Another method is based on the application of the sensitivity function.

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.

Shilnikov Chaos and Dynamics of a Self-Sustained Electromechanical Transducer

2000 ◽  
Vol 123 (2) ◽  
pp. 170-174 ◽  
Author(s):  
J. C. Chedjou ◽  
P. Woafo ◽  
S. Domngang
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Critical Points ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
The Stability

The dynamics of a self-sustained electromechanical transducer is studied. The stability of the critical points is analyzed using the analytic Routh-Hurwitz criterion. Analytic oscillatory solutions are obtained in both the resonant and non-resonant cases. Chaotic behavior is observed using the Shilnikov theorem and from a direct numerical simulation of the equations of motion.

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