| Full text | |
| Author(s): |
Perez, Otavio Henrique
;
Rondon, Gabriel
;
da Silva, Paulo Ricardo
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS; v. N/A, p. 18-pg., 2023-07-17. |
| Abstract | |
We study planar piecewise smooth differential systems of the form [GRAPHICS] . where F : R-2 -> R is a smooth map having 0 as a regular value. We consider linear regularizations Z(epsilon)(phi) of Z by replacing sgn(F) by phi(F/epsilon) in the last equation, with epsilon > 0 small and phi being a transition function (not necessarily monotonic). Nonlinear regularizations of the vector field Z whose transition function is monotonic are considered too. It is a wellknown fact that the regularized system is a slow-fast system. In this paper, we study typical singularities of slow-fast systems that arise from (linear or nonlinear) regularizations, namely, fold, transcritical and pitchfork singularities. Furthermore, the dependence of the slow-fast system on the graphical properties of the transition function is investigated. (AU) | |
| FAPESP's process: | 21/10198-9 - Invariant manifolds and limit periodic sets of discontinuous foliations |
| Grantee: | Otavio Henrique Perez |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| 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: | 22/12123-9 - Piecewise holomorphic systems and regularization of Filippov systems |
| Grantee: | Gabriel Alexis Rondón Vielma |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| FAPESP's process: | 20/06708-9 - Piecewise Holomorphic Systems and Regularization of Filippov fields around degenerated singularities and regular tangential polycycles |
| Grantee: | Gabriel Alexis Rondón Vielma |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 16/22310-0 - Discontinuous foliations and impasses |
| Grantee: | Otavio Henrique Perez |
| Support Opportunities: | Scholarships in Brazil - Doctorate |