Effects of Non-smooth Phenomena on the Dynamics of DC-DC Converters

2011 ◽  
Vol 29 (1) ◽  
pp. 119-122
Author(s):  
Dmitry Pikulin
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Bifurcation Analysis ◽  
Power Converters ◽  
Piecewise Linear ◽  
Nonlinear Phenomena ◽  
Switching Converters ◽  
Bifurcation Diagrams ◽  
Linear Dynamical Systems ◽  
Switch Mode

Effects of Non-smooth Phenomena on the Dynamics of DC-DC ConvertersThis paper provides the analysis of nonlinear phenomena in switch-mode power converters. In distinction to majority of known researches this paper presents novelty approach, allowing the complete bifurcation analysis, considering stable and various types of unstable behavior of nonlinear systems. Main results are illustrated on one of the most widely used switching converters - current controlled boost converter, for which the complete one-parametric bifurcation diagrams are constructed. The results include the detection of various types of rare attractors, smooth bifurcations and non-smooth phenomena, specific to piecewise linear dynamical systems.

scholarly journals Maximum number of limit cycles for certain piecewise linear dynamical systems

2015 ◽  
Vol 82 (3) ◽  
pp. 1159-1175 ◽  
Author(s):  
Jaume Llibre ◽  
Douglas D. Novaes ◽  
Marco A. Teixeira
Keyword(s):  
Dynamical Systems ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Linear Dynamical Systems

scholarly journals SELF-OSCILLATIONS AND SLIDING IN RELAY FEEDBACK SYSTEMS: SYMMETRY AND BIFURCATIONS

2001 ◽  
Vol 11 (04) ◽  
pp. 1121-1140 ◽  
Author(s):  
MARIO DI BERNARDO ◽  
KARL HENRIK JOHANSSON ◽  
FRANCESCO VASCA
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Bifurcation Analysis ◽  
Feedback System ◽  
Feedback Systems ◽  
Relay Feedback ◽  
Linear Dynamical Systems ◽  
Local Bifurcations

This paper is concerned with the bifurcation analysis of linear dynamical systems with relay feedback. The emphasis is on the bifurcations of the system periodic solutions and their symmetry. It is shown that, despite what has been conjectured in the literature, a symmetric and unforced relay feedback system can exhibit asymmetric periodic solutions. Moreover, the occurrence of periodic solutions characterized by one or more sections lying within the system discontinuity set is outlined. The mechanisms underlying their formation are carefully studied and shown to be due to an interesting, novel class of local bifurcations.

BIMODAL PIECEWISE LINEAR DYNAMICAL SYSTEMS: REDUCED FORMS

2010 ◽  
Vol 20 (09) ◽  
pp. 2795-2808 ◽  
Author(s):  
JOSEP FERRER ◽  
M. DOLORS MAGRET ◽  
MARTA PEÑA
Keyword(s):  
Dynamical Systems ◽  
Linear Systems ◽  
Piecewise Linear ◽  
Equivalence Classes ◽  
State Variables ◽  
Linear Dynamical Systems ◽  
Piecewise Linear Systems ◽  
Wide Range ◽  
General Systems ◽  
Reduced Forms

Piecewise linear systems constitute a class of nonlinear systems which have recently attracted the interest of researchers because of their interesting properties and the wide range of applications from which they arise. Different authors have used reduced forms when studying these systems, mostly in the case where they are observable. In this work, we focus on bimodal continuous dynamical systems (those consisting of two linear systems on each side of a given hyperplane, having continuous dynamics along that hyperplane) depending on two or three state variables, which are the most common piecewise linear systems found in practice. Reduced forms are obtained for general systems, not necessarily observable. As an application, we calculate the dimension of the equivalence classes.

Non-Stationary Oscillations at Slow Transitions Across Instabilities

2007 ◽  
Author(s):  
Rudolf R. Pusˇenjak ◽  
Maks M. Oblak ◽  
Jurij Avsec
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Time Scales ◽  
Primary Resonance ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Excitation Parameter ◽  
Linear Dynamical Systems ◽  
Weakly Nonlinear ◽  
Non Linear

The paper presents the study of non-stationary oscillations, which is based on extension of Lindstedt-Poincare (EL-P) method with multiple time scales for non-linear dynamical systems with cubic non-linearities. The generalization of the method is presented to discover the passage of weakly nonlinear systems through the resonance as a control or excitation parameter varies slowly across points of instabilities corresponding to the appearance of bifurcations. The method is applied to obtain non-stationary resonance curves of transition across points of instabilities during the passage through primary resonance of harmonically excited oscillators of Duffing type.

scholarly journals Breaking Points in Quartic Maps

2015 ◽  
Vol 25 (04) ◽  
pp. 1550051 ◽  
Author(s):  
M. Romera ◽  
G. Pastor ◽  
A. Martin ◽  
A. B. Orue ◽  
F. Montoya ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Abrupt Change ◽  
Iteration Process ◽  
Discrete Dynamical Systems ◽  
Nonlinear Phenomena ◽  
Bifurcation Diagrams ◽  
Quadratic Map ◽  
Breaking Points

Dynamical systems, whether continuous or discrete, are used by physicists in order to study nonlinear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some phenomena can depend alternatively on two values of the same parameter. We use the quadratic map [Formula: see text] when the parameter alternates between two values during the iteration process. In this case, the orbit of the alternate system is the sum of the orbits of two quartic maps. The bifurcation diagrams of these maps present breaking points at which there is an abrupt change in their evolution.

TWO-DIMENSIONAL BIFURCATION DIAGRAMS OF A CHAOTIC CIRCUIT BASED ON HYSTERESIS

2002 ◽  
Vol 12 (01) ◽  
pp. 43-69 ◽  
Author(s):  
FEDERICO BIZZARRI ◽  
MARCO STORACE
Keyword(s):  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Point Of View ◽  
Chaotic Oscillator ◽  
Circuit Parameter ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Analysis Point

This paper deals with the bifurcation analysis of a chaotic oscillator based on hysteresis. The analysis is carried out using two different models of the nonlinear resistive elements of the oscillator. The first model (more convenient from an analysis point of view) is piecewise linear (PWL), whereas the second (more realistic from a synthesis point of view) is smooth. For both models, the main results presented in this paper are two-dimensional bifurcation diagrams obtained for several values of a third circuit parameter.

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