On geometric structure of phase portraits of some piecewise linear dynamical systems

2021 ◽  
pp. 49-56
Author(s):  
V. P. Golubyatnikov ◽  
L. S. Minushkina
Keyword(s):  
Dynamical Systems ◽  
Geometric Structure ◽  
Piecewise Linear ◽  
Phase Portraits ◽  
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

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.

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.

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