The ranges of transfer and return maps in three-region piecewise-linear dynamical systems

1988 ◽  
Vol 16 (1) ◽  
pp. 11-23 ◽  
Author(s):  
Claus Kahlert
Keyword(s):  
Dynamical Systems ◽  
Piecewise Linear ◽  
Linear Dynamical Systems ◽  
Return Maps

THE EFFECTS OF SYMMETRY BREAKING IN CHUA'S CIRCUIT AND RELATED PIECEWISE-LINEAR DYNAMICAL SYSTEMS

1993 ◽  
Vol 03 (04) ◽  
pp. 963-979 ◽  
Author(s):  
CLAUS KAHLERT
Keyword(s):  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Piecewise Linear ◽  
Broken Symmetry ◽  
Chua’S Circuit ◽  
Intermediate Region ◽  
Linear Dynamical Systems ◽  
Chua's Circuit ◽  
Critical Curves ◽  
Return Maps

The behavior of transfer and return maps in the intermediate region of Chua's circuit and related systems undergoes a number of changes as the symmetry of the dynamics is broken, i.e., the separating planes are moved away from symmetric positions. We employ the technique of maps induced by the flow of the system and construct the critical curves for the maps in the intermediate region of state space. The influence of a broken symmetry on the critical curves and the flow is discussed in depth. We demonstrate that any breaking of symmetry potentially weakens and eventually destroys the chaos producing mechanisms.

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.

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