Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle–focus type

2019 ◽  
Vol 33 ◽  
pp. 162-178 ◽  
Author(s):  
Jiafu Wang ◽  
Chuangxia Huang ◽  
Lihong Huang
Keyword(s):  
Linear System ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Piecewise Linear System ◽  
Focus Type

Realization of Arbitrary Configuration of Limit Cycles of Piecewise Linear Systems

2020 ◽  
Vol 30 (09) ◽  
pp. 2050133
Author(s):  
Shaoqing Wang ◽  
Jiazhong Yang
Keyword(s):  
Linear System ◽  
Finite Number ◽  
Linear Systems ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Continuous Curve ◽  
Jordan Curves ◽  
Piecewise Linear Systems ◽  
Piecewise Linear System ◽  
Arbitrary Configuration

In this paper, we consider the realization of configuration of limit cycles of piecewise linear systems on the plane. We show that any configuration of finite number of Jordan curves can be realized by a discontinuous piecewise linear system with two zones separated by a continuous curve.

scholarly journals A Simple Solution to the Braga–Mello Conjecture

2015 ◽  
Vol 25 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Douglas D. Novaes ◽  
Enrique Ponce
Keyword(s):  
Linear System ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Simple Solution ◽  
Piecewise Linear System

Recently Braga and Mello conjectured that for a given n ∈ ℕ there is a piecewise linear system with two zones in the plane with exactly n limit cycles. In this paper, we prove a result from which the conjecture is an immediate consequence. Several explicit examples are given where location and stability of limit cycles are provided.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System
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