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.

Dynamics of an Electromechanical System With Angular and Ferroresonant Nonlinearities

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
D. O. Tcheutchoua Fossi ◽  
P. Woafo
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Harmonic Balance ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Electromechanical System ◽  
Bifurcation Diagrams ◽  
Oscillatory Solutions ◽  
Torsion Bar ◽  
Hysteresis Phenomena

The purpose of this paper is to study the dynamics of an electromechanical system consisting of a torsion-bar or two mechanical pumps activated by an electromotor. Oscillatory solutions showing the jump and hysteresis phenomena are obtained using the harmonic balance method and direct numerical simulation. Chaotic behavior is presented via the bifurcation diagrams and corresponding Lyapunov exponent. Some implications of the results on the applications of the devices are discussed.

scholarly journals Dynamic Effects Arise Due to Consumers’ Preferences Depending on Past Choices

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 173 ◽  
Author(s):  
Sameh S. Askar ◽  
A. Al-khedhairi
Keyword(s):  
Numerical Simulation ◽  
Fixed Points ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Dynamic Effects ◽  
One Dimensional ◽  
First Case ◽  
The Stability ◽  
Conditions Of Stability ◽  
Dynamic Duopoly

We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb–Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game’s map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game’s parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game’s map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case.

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

Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2. The lobe-and-cleft instability

2000 ◽  
Vol 418 ◽  
pp. 213-229 ◽  
Author(s):  
CARLOS HÄRTEL ◽  
FREDRIK CARLSSON ◽  
MATTIAS THUNBLOM
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Direct Numerical Simulation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Gravity Current ◽  
Leading Edge ◽  
Two Dimensional ◽  
Amplification Rate ◽  
The Stability

Results are presented from a linear-stability analysis of the flow at the head of two-dimensional gravity-current fronts. The analysis was undertaken in order to clarify the instability mechanism that leads to the formation of the complex lobe-and-cleft pattern which is commonly observed at the leading edge of gravity currents propagating along solid boundaries. The stability analysis concentrates on the foremost part of the front, and is based on direct numerical simulation data of two-dimensional lock-exchange flows which are described in the companion paper, Härtel et al. (2000). High-order compact finite differences are employed to discretize the stability equations which results in an algebraic eigenvalue problem for the amplification rate, that is solved in an iterative fashion. The analysis reveals the existence of a vigorous linear instability that acts in a localized way at the leading edge of the front and originates in an unstable stratification in the flow region between the nose and stagnation point. It is shown that the amplification rate of this instability as well as its spanwise length scale depend strongly on Reynolds number. For validation, three-dimensional direct numerical simulations of the early stages of the frontal instability are performed, and close agreement with the results from the linear-stability analysis is demonstrated.

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

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