More Than Three Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Zones in the Plane-Reference-Cited by-同舟云学术

More Than Three Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Zones in the Plane

Published:2014-04 Issue:04 Volume:24 Page:1450056
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Braga Denis De Carvalho¹,Mello Luis Fernando²

Affiliation:

1. Campus Avançado de Itabira, Universidade Federal de Itajubá, Rua São Paulo 377, Bairro Amazonas, CEP 35.900–373, Itabira, MG, Brazil

2. Instituto de Matemática e Computação, Universidade Federal de Itajubá, Avenida BPS 1303, Pinheirinho, CEP 37.500–903, Itajubá, MG, Brazil

Abstract

In this paper, we study the existence of limit cycles for piecewise linear differential systems with two zones in the plane. More precisely, we prove the existence of piecewise linear differential systems with two zones in the plane with four, five, six and seven limit cycles. From our results we conjecture the existence of piecewise linear differential systems with two zones in the plane having exactly n limit cycles for all n ∈ ℕ.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127414500564

Reference9 articles.

1. THE METHOD OF THE POINT TRANSFORMATIONS IN PIECE-WISE LINEAR SYSTEMS

2. Limit cycles in a family of discontinuous piecewise linear differential systems with two zones in the plane

3. CHUA’S CIRCUIT: AN OVERVIEW TEN YEARS LATER

4. Canonical Discontinuous Planar Piecewise Linear Systems

5. On the number of limit cycles in general planar piecewise linear systems

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