| Full text | |
| Author(s): |
Andrade, Kamila S.
;
Gomide, Otavio M. L.
;
Novaes, Douglas D.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | NONLINEAR ANALYSIS-HYBRID SYSTEMS; v. 50, p. 26-pg., 2023-11-01. |
| Abstract | |
In this paper, we are concerned about the qualitative behavior of planar Filippov systems around some typical invariant 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 Filippov 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 apply this method to describe bifurcation diagrams of Filippov systems around certain polycycles.& COPY; 2023 Elsevier Ltd. All rights reserved. (AU) | |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 15/22762-5 - Structural Stability of Nonsmooth Systems on Tridimensional Manifolds |
| Grantee: | Otávio Marçal Leandro Gomide |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 22/09633-5 - Averaging theory for studying invariant tori and periodic behavior in differential equations and inclusions |
| Grantee: | Douglas Duarte Novaes |
| Support Opportunities: | Regular Research Grants |