1.
Kamila S. Andrade; Otávio M.L. Gomide; Douglas D. Novaes; Marco A. Teixeira
Bifurcation Diagrams of Global Connections in Filippov Systems Journal Article
Em: Nonlinear Analysis: Hybrid Systems, vol. 50, pp. 101397, 2023.
@article{AndGomNov2023,
title = {Bifurcation Diagrams of Global Connections in Filippov Systems},
author = {Kamila S. Andrade and Otávio M.L. Gomide and Douglas D. Novaes and Marco A. Teixeira },
url = {http://arxiv.org/abs/1905.11950},
doi = {10.1016/j.nahs.2023.101397},
year = {2023},
date = {2023-11-01},
urldate = {2023-11-01},
journal = {Nonlinear Analysis: Hybrid Systems},
volume = {50},
pages = {101397},
abstract = {In this paper, we are concerned about the qualitative behaviour of planar Filippov systems around some typical minimal sets, namely, polycycles. In the smooth context, a polycycle is a simple closed curve composed by a collection of singularities and regular orbits, inducing a first return map. Here, this concept is extended to Filippov systems by allowing typical singularities lying on the switching manifold. Our main goal consists in developing a method to investigate the unfolding of polycycles in Filippov systems. In addition, we applied this method to describe bifurcation diagrams of Filippov systems around certain polycycles. },
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this paper, we are concerned about the qualitative behaviour of planar Filippov systems around some typical minimal sets, namely, polycycles. In the smooth context, a polycycle is a simple closed curve composed by a collection of singularities and regular orbits, inducing a first return map. Here, this concept is extended to Filippov systems by allowing typical singularities lying on the switching manifold. Our main goal consists in developing a method to investigate the unfolding of polycycles in Filippov systems. In addition, we applied this method to describe bifurcation diagrams of Filippov systems around certain polycycles.
