scholarly journals Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve

2021 ◽  
Vol 287 ◽  
pp. 1-36
Author(s):  
Kamila da S. Andrade ◽  
Oscar A.R. Cespedes ◽  
Dayane R. Cruz ◽  
Douglas D. Novaes
Keyword(s):  
Vector Fields ◽  
Piecewise Linear ◽  
Higher Order ◽  
Linear Vector ◽  
Switching Curve ◽  
Melnikov Analysis ◽  
Nonlinear Switching

scholarly journals Higher Order Singularities in Piecewise Linear Vector Fields

2000 ◽  
pp. 99-113 ◽  
Author(s):  
Xavier Tricoche ◽  
Gerik Scheuermann ◽  
Hans Hagen
Keyword(s):  
Vector Fields ◽  
Piecewise Linear ◽  
Higher Order ◽  
Linear Vector

N-DIMENSIONAL CANONICAL CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 239-258 ◽  
Author(s):  
LJ. KOCAREV ◽  
LJ. KARADZINOV ◽  
L. O. CHUA
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Measure Zero ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Continuous Vector ◽  
Linear Vector ◽  
Linear Dynamic ◽  
Canonical Chua’S Circuit

In this paper we present an n-dimensional canonical piecewise-linear electrical circuit. It contains 2n two-terminal elements: n linear dynamic elements (capacitors and inductors), n - 1 linear resistors and one nonlinear (piecewise-linear) resistor. This circuit can realize any prescribed eigenvalue pattern, except for a set of measure zero, associated with (i) any n-dimensional two-region continuous piecewise-linear vector fields and (ii) any n-dimensional three-region symmetric (with respect to the origin) piecewise-linear continuous vector fields. We also proved a theorem that specifies the conditions for a vector field, realized with our canonical circuit, to have two or three equilibrium points.

Limit Cycles Bifurcating from a Period Annulus in Continuous Piecewise Linear Differential Systems with Three Zones

2017 ◽  
Vol 27 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Maurício Firmino Silva Lima ◽  
Claudio Pessoa ◽  
Weber F. Pereira
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Poincaré Map ◽  
Piecewise Linear ◽  
Differential Systems ◽  
Linear Vector ◽  
Period Annulus ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Two Parameter

We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits at least two limit cycles that appear by perturbations of a period annulus. Moreover, we describe the bifurcation of the limit cycles for this class through two examples of two-parameter families of piecewise linear vector fields with three zones.

scholarly journals Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces

2006 ◽  
Vol 12 (5) ◽  
pp. 1315-1322 ◽  
Author(s):  
Wan-chiu Li ◽  
Bruno Vallet ◽  
Nicolas Ray ◽  
Bruno Levy
Keyword(s):  
Vector Fields ◽  
Piecewise Linear ◽  
Higher Order

scholarly journals LIMIT CYCLES FOR A CLASS OF CONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH THREE ZONES

2012 ◽  
Vol 22 (06) ◽  
pp. 1250138 ◽  
Author(s):  
MAURÍCIO FIRMINO SILVA LIMA ◽  
JAUME LLIBRE
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Vector Fields ◽  
Poincaré Map ◽  
Piecewise Linear ◽  
Differential Systems ◽  
Linear Vector ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Unique Limit

In this paper, we consider a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map, we show that these systems admit always a unique limit cycle, which is hyperbolic.

BIFURCATION SETS OF SYMMETRICAL CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH THREE ZONES

2002 ◽  
Vol 12 (08) ◽  
pp. 1675-1702 ◽  
Author(s):  
EMILIO FREIRE ◽  
ENRIQUE PONCE ◽  
FRANCISCO RODRIGO ◽  
FRANCISCO TORRES
Keyword(s):  
Linear Systems ◽  
Canonical Form ◽  
Vector Fields ◽  
Piecewise Linear ◽  
Oscillatory Behavior ◽  
Van Der Pol ◽  
Linear Vector ◽  
Piecewise Linear Systems

Planar symmetrical continuous piecewise linear vector fields with three zones are thoroughly analyzed. Special emphasis is placed on their oscillatory behavior. The study is made by using a Van der Pol canonical form which captures the most interesting dynamics and minimizes the number of parameters to be dealt with. This work is a continuation of a previous paper [Freire et al., 1998] and uses the same approach and techniques.

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