ONE-DIMENSIONAL DYNAMICS OF THE VAN DER POL CIRCUIT

2012 ◽  
Vol 22 (12) ◽  
pp. 1250306
Author(s):  
JACEK KUDREWICZ
Keyword(s):  
Relaxation Oscillator ◽  
Discontinuity Point ◽  
Jump Discontinuity ◽  
Voltage Source ◽  
Sinusoidal Voltage ◽  
Van Der Pol ◽  
One Dimensional ◽  
Border Collision Bifurcations ◽  
Neon Lamp ◽  
Rotation Numbers

The van der Pol circuit with neon glow lamp operates as a relaxation oscillator driven by a sinusoidal voltage source. Its dynamics is described by the function which maps an arc of circle into itself, preserves orientation on this arc, and has at most one jump-discontinuity point on the circle. Properties of this mapping are discussed with emphasis on rotation numbers, types of periodic orbits, saddle-node and border-collision bifurcations. The so-called period-adding phenomenon is explained. Some remarks are given about dynamics, where the mapping does not preserve the orientation because of too long neon lamp lighting.

PERIOD ADDING IN PIECEWISE LINEAR MAPS WITH TWO DISCONTINUITIES

2012 ◽  
Vol 22 (03) ◽  
pp. 1250068 ◽  
Author(s):  
FABIO TRAMONTANA ◽  
LAURA GARDINI ◽  
VIKTOR AVRUTIN ◽  
MICHAEL SCHANZ
Keyword(s):  
Piecewise Linear ◽  
Discontinuity Point ◽  
Big Bang ◽  
One Dimensional ◽  
Piecewise Linear Map ◽  
Stable Regime ◽  
Bifurcation Points ◽  
Border Collision Bifurcations ◽  
Linear Maps ◽  
Piecewise Linear Maps

In this work we consider the border collision bifurcations occurring in a one-dimensional piecewise linear map with two discontinuity points. The map, motivated by an economic application, is written in a generic form and considered in the stable regime, with all slopes between zero and one. We prove that the period adding structures occur in maps with more than one discontinuity points and that the Leonov's method to calculate the bifurcation curves forming these structures is applicable also in this case. We demonstrate the existence of particular codimension-2 bifurcation (big-bang bifurcation) points in the parameter space, from which infinitely many bifurcation curves are issuing associated with cycles involving several partitions. We describe how the bifurcation structure of a map with one discontinuity is modified by the introduction of a second discontinuity point, which causes orbits to appear located on three partitions and organized again in a period-adding structure. We also describe particular codimension-2 bifurcation points which represent limit sets of doubly infinite sequences of bifurcation curves and appear due to the existence of two discontinuities.

Codimension-2 Border Collision, Bifurcations in One-Dimensional, Discontinuous Piecewise Smooth Maps

2014 ◽  
Vol 24 (02) ◽  
pp. 1450024 ◽  
Author(s):  
Laura Gardini ◽  
Viktor Avrutin ◽  
Irina Sushko
Keyword(s):  
Discontinuity Point ◽  
Piecewise Smooth ◽  
One Dimensional ◽  
Smooth Maps ◽  
Border Collision Bifurcations ◽  
Piecewise Smooth Maps ◽  
Symbolic Sequences ◽  
Bifurcation Structures ◽  
Local Monotonicity ◽  
Parameter Values

We consider a two-parametric family of one-dimensional piecewise smooth maps with one discontinuity point. The bifurcation structures in a parameter plane of the map are investigated, related to codimension-2 bifurcation points defined by the intersections of two border collision bifurcation curves. We describe the case of the collision of two stable cycles of any period and any symbolic sequences. For this case, we prove that the local monotonicity of the functions constituting the first return map defined in a neighborhood of the border point at the parameter values related to the codimension-2 bifurcation point determines, under suitable conditions, the kind of bifurcation structure originating from this point; this can be either a period adding structure, or a period incrementing structure, or simply associated with the coupling of colliding cycles.

Battery Losses In a MMC for BEVS Application

2018 ◽  
Vol 12 (1) ◽  
pp. 98-109 ◽  
Author(s):  
Adolfo Dannier ◽  
Gianluca Brando ◽  
Ivan Spina ◽  
Diego Iannuzzi
Keyword(s):  
Mathematical Model ◽  
System Architecture ◽  
Electrochemical Cell ◽  
Voltage Source ◽  
Modular Multilevel Converter ◽  
Voltage Reference ◽  
Sinusoidal Voltage ◽  
Current Waveform ◽  
Voltage Source Inverter ◽  
Multilevel Converter

Objective:This paper analyses the Modular Multilevel Converter (MMC) topology, where each individual Sub Module (SM), in half bridge configuration, is directly fed by an elementary electrochemical cell.Methods:The aim is to investigate how the reference voltages influence the cells currents waveforms, determining how the active powers and the losses are distributed among the cells. Considering a 2-level Voltage Source Inverter (VSI) topology working in the same conditions, the ratio between the MMC total cells losses and VSI total cells losses is calculated. After showing the system architecture and mathematical model, the cells current waveform investigation is presented and detailed both for triangular and sinusoidal voltage reference waveform.Results:Finally, the results are critically discussed with particular focus on the comparison between the MMC and the VSI topologies.

scholarly journals Transient Current Density in a Pair of Long Parallel Conductors

2021 ◽  
Vol 11 (15) ◽  
pp. 6920
Author(s):  
Oldřich Coufal
Keyword(s):  
Steady State ◽  
Cross Section ◽  
Current Density ◽  
Circular Cross Section ◽  
Transient Current ◽  
Constant Current ◽  
Voltage Source ◽  
Sinusoidal Voltage ◽  
Steady State Current ◽  
Maximum Current

Two infinitely long parallel conductors of arbitrary cross section connected to a voltage source form a loop. If the source voltage depends on time, then due to induction there is no constant current density in the loop conductors. It is only recently that a method has been published for accurately calculating current density in a group of long parallel conductors. The method has thus far been applied to the calculation of steady-state current density in a loop connected to a sinusoidal voltage source. In the present article, the method is used for an accurate calculation of transient current using transient current density. The transient current is analysed when connecting and short-circuiting the sources of sinusoidal, constant and sawtooth voltages. For circular cross section conductors, the dependences of maximum current density, maximum current and the time of achieving steady state on the source frequency, the distance of the conductors and their resistivity when connecting the source of sinusoidal voltage are examined.

Self-induction in two long parallel conductors connected to sinusoidal voltage source

2020 ◽  
Vol 95 (6) ◽  
pp. 065503
Author(s):  
Oldřich Coufal ◽  
Lukáš Radil
Keyword(s):  
Voltage Source ◽  
Sinusoidal Voltage

A Low Frequency Sinusoidal Voltage Source

1950 ◽  
Vol 21 (4) ◽  
pp. 302-303
Author(s):  
Louis A. Rosenthal
Keyword(s):  
Low Frequency ◽  
Voltage Source ◽  
Sinusoidal Voltage

scholarly journals Modernization of a frequency-controlled asynchronous electric drive system

2019 ◽  
pp. 25-33
Author(s):  
I. V. Shestakov ◽  
N. R. Safin
Keyword(s):  
Energy Efficiency ◽  
Electric Drive ◽  
Asynchronous Motor ◽  
Operating Mode ◽  
Voltage Source ◽  
Sinusoidal Voltage ◽  
Pulse Width Modulated ◽  
Operating Modes ◽  
Asynchronous Electric Drive ◽  
Research Show

The paper introduces the results of mathematical simulation of the operating modes of an asynchronous motor when powered by a sinusoidal voltage source and a width-modulated voltage pulse source. The study shows the possibilities of increasing the energy efficiency of an asynchronous electric drive. Findings of research show the feasibility of studying the switching of the motor power source from a pulse width-modulated voltage to a sinusoidal voltage source in the nominal operating mode in order to increase the energy efficiency of the electric drive

scholarly journals Parabolic bursting, spike-adding, dips and slices in a minimal model

2019 ◽  
Vol 14 (4) ◽  
pp. 406
Author(s):  
Mathieu Desroches ◽  
Jean-Pierre Francoise ◽  
Martin Krupa
Keyword(s):  
Qualitative Analysis ◽  
Numerical Simulations ◽  
Phase Portrait ◽  
Minimal Model ◽  
Bifurcation Theory ◽  
Minimal System ◽  
Dimensional System ◽  
Slow Flow ◽  
Van Der Pol ◽  
One Dimensional

A minimal system for parabolic bursting, whose associated slow flow is integrable, is presented and studied both from the viewpoint of bifurcation theory of slow-fast systems, of the qualitative analysis of its phase portrait and of numerical simulations. We focus the analysis on the spike-adding phenomenon. After a reduction to a periodically forced one-dimensional system, we uncover the link with the dips and slices first discussed by J.E. Littlewood in his famous articles on the periodically forced van der Pol system.

PACKING SUBORDINACY WITH APPLICATION TO SPECTRAL CONTINUITY

2019 ◽  
Vol 108 (2) ◽  
pp. 226-244 ◽  
Author(s):  
V. R. BAZAO ◽  
S. L. CARVALHO ◽  
C. R. DE OLIVEIRA
Keyword(s):  
Continuous Spectrum ◽  
Dimensional Stability ◽  
Schrödinger Operators ◽  
Stability Result ◽  
Schrodinger Operators ◽  
Spectral Measures ◽  
One Dimensional ◽  
Continuity Properties ◽  
Rotation Numbers ◽  
Spectral Continuity

By using methods of subordinacy theory, we study packing continuity properties of spectral measures of discrete one-dimensional Schrödinger operators acting on the whole line. Then we apply these methods to Sturmian operators with rotation numbers of quasibounded density to show that they have purely $\unicode[STIX]{x1D6FC}$-packing continuous spectrum. A dimensional stability result is also mentioned.

Sign in / Sign up

Export Citation Format

Share Document