scholarly journals Evidence of Strange Attractors in Class C Amplifier with Single Bipolar Transistor: Polynomial and Piecewise-Linear Case

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 175
Author(s):  
Jiri Petrzela
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Experimental Measurement ◽  
Piecewise Linear ◽  
Bipolar Transistor ◽  
Sufficient Condition ◽  
Complex Behavior ◽  
Transient Motion ◽  
Network Topologies ◽  
Bias Point

This paper presents and briefly discusses recent observations of dynamics associated with isolated generalized bipolar transistor cells. A mathematical model of this simple system is considered on the highest level of abstraction such that it comprises many different network topologies. The key property of the analyzed structure is its bias point since the transistor is modeled via two-port admittance parameters. A necessary but not sufficient condition for the evolution of autonomous complex behavior is the nonlinear bilateral nature of the transistor with arbitrary reason that causes this effect. It is proved both by numerical analysis and experimental measurement that chaotic motion is miscellaneous, robust, and it is neither numerical artifact nor long transient motion.

scholarly journals Local and global stability of a piecewise linear oscillator

1992 ◽  
Vol 338 (1651) ◽  
pp. 533-546 ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Nonlinear Oscillator ◽  
Dynamic Behaviour ◽  
Piecewise Linear ◽  
Global Bifurcation ◽  
Simple Mathematical Model ◽  
Periodic Excitation ◽  
Restoring Force ◽  
Modern Methods

Machines and mechanisms with moving parts, subjected to periodic excitation, often show unexpected dynamic behaviour, and impacts due to their connection clearances may occur. The most simple mathematical model is a one degree-of-freedom nonlinear oscillator governed by a piecewise linear symmetric function to describe the restoring force. The system’s response, which can be quite rich and complicated, is described in detail. Modern methods for a combined analytical and numerical analysis are used to study local and global bifurcation conditions, coexisting solutions and their associated domains of attraction.

scholarly journals Theoretical and numerical analysis of novel COVID-19 via fractional order mathematical model

2021 ◽  
Vol 20 ◽  
pp. 103676
Author(s):  
Amjad Ali ◽  
Muhammad Yasin Khan ◽  
Muhammad Sinan ◽  
F.M. Allehiany ◽  
Emad E. Mahmoud ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Fractional Order ◽  
Theoretical And Numerical Analysis

The Numerical Analysis of the Velocity and Pressure Distribution of the Oil Film in Heavy Hydrostatic Thrust Bearing

2014 ◽  
Vol 541-542 ◽  
pp. 658-662
Author(s):  
Jian Li ◽  
Yuan Chen ◽  
Yang Chun Yu ◽  
Zhu Xin Tian ◽  
Yu Huang
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Pressure Distribution ◽  
Working Conditions ◽  
Thrust Bearing ◽  
Rotation Speed ◽  
The Other ◽  
Surface Load ◽  
Oil Film ◽  
Volume Method

To study the velocity and pressure distribution of the oil film in a heavy hydrostatic thrust bearing, a mathematical model of the velocity is proposed and the finite volume method (FVM) has been used to simulate the flow field under different working conditions. Some pressure experiments were carried out and the results verified the correctness of the simulation. It is concluded that the pressure distribution varies small under different rotation speed when the surface load on the workbench is constant. But the velocity of the oil film is influenced greatly by the rotation speed. When the rotation speed of the workbench is as quick as enough, the velocity of the oil film on one radial side of the pad will be zero, that is to say the lubrication oil will be drained from the other three sides of the recess.

State Estimator of Flow as an Integrated Computational Method With the Feedback of Online Experimental Measurement

1997 ◽  
Vol 119 (4) ◽  
pp. 814-822 ◽  
Author(s):  
Toshiyuki Hayase ◽  
Satoru Hayashi
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Experimental Measurement ◽  
Flow Simulation ◽  
Computational Method ◽  
Feedback Gain ◽  
State Estimator ◽  
Output Measurement ◽  
Real Flow ◽  
The Mathematical Model

This paper deals with a state estimator or simply an observer of flow field. The observer, being a fundamental concept in the control system theory, also has a potential in the analysis of flow related problems as an integrated computational method with the aid of experiment. In the framework of the observer, the state of physical flow is estimated from the mathematical model with the feedback of on-line experimental measurement. A SIMPLER based flow simulation algorithm is used as the mathematical model of the real flow and partial experimental measurement of flow is fed back to the boundary condition through the feedback controller. The existence of the feedback-loop essentially distinguishes the observer from ordinary flow simulations. Time variation of the computational result of the observer is expected to converge exactly to that of the physical flow in the whole flow domain even for unstable turbulent flows. A numerical experiment has been performed to confirm the validity of the proposed observer for a turbulent flow through a duct of square cross section. The physical flow to be estimated is modeled by a numerical solution. Appropriate choice for the proportional feedback gain of the observer results in accelerated convergence of the simulation by a factor of 0.012 and reduced error in estimation of the perturbation velocity by a factor of 0.6 in the whole domain or a factor of 0.3 behind the output measurement plane in comparison with the ordinary flow simulation without feedback.

Numerical analysis of distortion characteristics of heterojunction bipolar transistor laser

2015 ◽  
Vol 357 ◽  
pp. 177-184 ◽  
Author(s):  
S. Piramasubramanian ◽  
M. Ganesh Madhan ◽  
Jyothsna Nagella ◽  
G. Dhanapriya
Keyword(s):  
Numerical Analysis ◽  
Bipolar Transistor ◽  
Heterojunction Bipolar Transistor ◽  
Transistor Laser

scholarly journals Positive Normalization of Discrete Descriptor System under Disturbance

MATEMATIKA ◽  
2018 ◽  
Vol 34 (3) ◽  
pp. 141-147
Author(s):  
Ahmad Iqbal Baqi ◽  
Admi Nazra ◽  
Zulakmal Zulakmal ◽  
Lyra Yulianti ◽  
Muhafzan Muhafzan
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Unique Solution ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Real Problem ◽  
Sufficient Condition ◽  
Input Output ◽  
Application Field

It is well known the descriptor systems have a wide application field. Usually it appear as a mathematical model of a real problem, mainly the model that involves the input output relationship. It is well known that a descriptor linear system has an unique solution if the pencil matrix of the system is regular. However, there are some systems that are not regular. Moreover, even though the system is regular the solution can contain the noncausal behavior. Therefore, it is necessary to normalize the descriptor system so as it has well behavior. In this paper, we propose a feedback to normalize a discrete descriptor system under disturbance. Furthermore, we establish a sufficient condition in order for the discrete descriptor system under disturbance can be normalized positively.

HYPERCHAOS IN A MODIFIED CANONICAL CHUA'S CIRCUIT

2004 ◽  
Vol 14 (01) ◽  
pp. 221-243 ◽  
Author(s):  
K. THAMILMARAN ◽  
M. LAKSHMANAN ◽  
A. VENKATESAN
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Laboratory Experiments ◽  
System Parameter ◽  
Piecewise Linear ◽  
Electrical Circuit ◽  
First Order ◽  
Regular Behavior ◽  
Linear Elements

In this paper, we present the hyperchaos dynamics of a modified canonical Chua's electrical circuit. This circuit, which is capable of realizing the behavior of every member of the Chua's family, consists of just five linear elements (resistors, inductors and capacitors), a negative conductor and a piecewise linear resistor. The route followed is a transition from regular behavior to chaos and then to hyperchaos through border-collision bifurcation, as the system parameter is varied. The hyperchaos dynamics, characterized by two positive Lyapunov exponents, is described by a set of four coupled first-order ordinary differential equations. This has been investigated extensively using laboratory experiments, Pspice simulation and numerical analysis.

Design of a New Multi-Channel High-Low Pressure Micro-Ejection System

2011 ◽  
Vol 189-193 ◽  
pp. 4313-4317
Author(s):  
Wei Yang ◽  
Qiang Yin ◽  
Kun Wang Niu ◽  
Jiao Zhang ◽  
Wen Dong Zhang
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Structural Design ◽  
Structural Characteristics ◽  
Low Pressure ◽  
Classical Trajectory ◽  
Design Methods ◽  
Analysis And Design ◽  
Bullet Velocity

According to the structural characteristics of the multi-channel high-low pressure micro-ejection system,this paper sets up mathematical model of the trajectory based on the classical trajectory theory,makes numerical analysis to prove the rationality of the structural design,tests the pressure and bullet velocity of the launching system.The results show that the analysis and design methods of the multi-channel high-low pressure micro-ejection system are reasonable and reliable.

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