At most two limit cycles in a piecewise linear differential system with three zones and asymmetry

2019 ◽  
Vol 386-387 ◽  
pp. 23-30 ◽  
Author(s):  
Hebai Chen ◽  
Yilei Tang
Keyword(s):  
Differential System ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Linear Differential System ◽  
Piecewise Linear Differential System ◽  
Linear Differential

scholarly journals Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by reducible cubics

2021 ◽  
pp. 1-38
Author(s):  
Rebiha Benterki ◽  
Jeidy Jimenez ◽  
Jaume Llibre
Keyword(s):  
Hamiltonian Systems ◽  
Differential System ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Main Role ◽  
Differential Systems ◽  
Cubic Curve ◽  
Straight Line ◽  
Linear Hamiltonian Systems ◽  
Linear Differential

Due to their applications to many physical phenomena during these last decades the interest for studying the discontinuous piecewise differential systems has increased strongly. The limit cycles play a main role in the study of any planar differential system, but to determine the maximum number of limits cycles that a class of planar differential systems can have is one of the main problems in the qualitative theory of the planar differential systems. Thus in general to provide a sharp upper bound for the number of crossing limit cycles that a given class of piecewise linear differential system can have is a very difficult problem. In this paper we characterize the existence and the number of limit cycles for the piecewise linear differential systems formed by linear Hamiltonian systems without equilibria and separated by a reducible cubic curve, formed either by an ellipse and a straight line, or by a parabola and a straight line parallel to the tangent at the vertex of the parabola. Hence we have solved the extended 16th Hilbert problem to this class of piecewise differential systems.

scholarly journals On a linear differential system of neutral type

1986 ◽  
Vol 40 (2) ◽  
pp. 226-233
Author(s):  
P. Ch. Tsamatos
Keyword(s):  
Fixed Points ◽  
Differential System ◽  
Finite Dimension ◽  
Neutral Type ◽  
Common Fixed Points ◽  
Linear Differential System ◽  
Linear Differential

AbstractThis paper is concerned with the neutral type differential system with derivating arguments. By decomposing the space of initial functions into classes, it is derived that, for each class, the space of corresponding solutions is of finite dimension. The case of common fixed points of the arguments is also studied.

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